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sychological  Review  Monograph  No.  69 


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uracy  of  the  Voice  in  Simple 
Pitch  Singing 


BY 


WALTER  R.  MILES 


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Reprinted  from  Psychological  Review  Monograph  No.  69 


Accuracy  of  the  Voice  in  Simple 
Pitch  Singing 


BY 

WALTER  R.  MILES 


Reprinted  from   Psychological  Review  Monograph  No.  69 


Accuracy  of  the  Voice  in  Simple 

Pitch  Singing 


I  M^SiC  LIBKARV  j 
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BY 

WALTER  R.  MILES 


A  thesis  submitted  to  the  Department  of  Philosophy  and  Psy- 
chology of  the  Graduate  College  in  the  State  University  of 
Iowa,  in  partial  fulfillment  of  the  Requirement  for  the  degree 
of  Doctor  of  Philosophy. 


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ACCURACY  OF  THE  VOICE  IN  SIMPLE  PITCH  SINGING 

BY 
WALTER    R.    MILES 

Contents 

Historical 
The  tonoscope 

Experiments  Series  I :  accuracy  and  the  voice  range 
Experiments  Series  II :  intensity   of   standard 
Experiments  Series  III :  volume  of  the  voice 
Experiments  Series  IV:  timbre  of  standard  tones 
Experiments  Series  V :  vowel  quality  and  accuracy 
Experiments  Series  VI :  accuracy  in  singing 

Apparatus  and   method :   standards,   observers,  the  charge,  the  test. 

Justification  of  procedure :  voice  level  of  test,  forks  for  standards, 
many  standards  vs.  one  standard,  sounding  the  two  tones,  order 
of  standards,  time  intervals,  other  factors 

Tables  of  data. 

Comparison  of  the  abilities  of  men  and  women 

The  mean  variation 

The  constant  error 

The  group  constant  error 

The  best  cases 

Correlation  of  singing  with   pitch   discrimination 
The  test  of  1910 
Recommendations 
Summary  of  conclusions 
References 

The  experiments  here  reported  deal  with  two  phases  of  simple 
pitch  singing:  (i)  the  ability  of  the  voice  to  reproduce  the  pitch 
of  a  tone,  and  (2)  the  ability  to  matce  faint  shadings  in  pitch,  sharp 
or  flat.  The  aim  has  been  to  formulate,  if  possible,  a  standard 
test  for  the  measurement  of  each,  to  establish  norms,  an3  to  investi- 
gate some  of  the  underlying  psychological  factors.^ 

'  The  extensive  measurements  made  would  have  been  impossible  were  it  not 
for  the  previous  labor  of  Professor  Seashore  in  perfecting  a  recording  appara- 
tus, the  Tonoscope.  Dr.  Seashore  has  furthermore  proved  himself  an  unfail- 
ing source  of  inspiration  and  suggestion  throughout  the  experimentation. 
The  author  is  also  under  heavy  obligations  to  Assistant  Professor  Mabel  C. 
Williams,  Dr.  Thomas  F.  Vance,  Messrs.  Bruene  and  Malmberg,  and  the 
many  observers  for  their  kind  and  prolonged  assistance. 


^i^4iV8 


HISTORICAL 

The  first  investigator  to  employ  the  experimental  method  in 
attacking  the  problem  of  the  accuracy  of  the  voice  in  singing  pitch 
was  Kliinder  (ii)  1872.-  He  used  a  manometric  flame  with  two 
connected  speaking  tubes,  an  organ  tone  sounding  in  one  while  the 
observer  sang  simultaneously  in  the  other.  The  difference  in 
vibration  number  between  the  standard  and  sung  tones  was  de- 
termined by  counting  waves.  The  average  rh  errors  found  on  three 
tones,  128,  192,  256,  v.d.  are  0.761,  0.434,  and  0.257  per  cent. 
(of  standards)  respectively.  The  difference  between  0.761  and  0.257 
was  thought  to  be  due  to  the  vocal  cords  and  not  to  hearing. 

Kliinder  was  not  satisfied  with  his  method  or  his  results  and  con- 
tinued working  on  the  problem,  publishing  a  second  time  in  1879 
(12).  Again  he  used  organ  tones  as  standards  and  had  his  ob- 
servers sing  simultaneously  with  them,  either  in  unison  or  in  speci- 
fied interval.  The  recording  was  done  on  smoked  paper  by  means 
of  two  phonautographs.  The  two  records  were  compared  directly, 
that  for  the  organ  tone  being  used  as  a  standard,  and  deviation  in 
the  pitch  of  the  voice  from  that  of  the  standard  was  computed  in 
terms  of  .25  v.d.  That  Kliinder  was  primarily  interested  in  the 
physiological  side  of  the  problem  is  indicated  by  the  questions 
which  he  set  himself: 

(i)  Does  our  ear  control  the  voice  or  is  it  controlled  by  the 
feeling  of  tension  in  the  larynx?  (2)  How  firmly  does  the  voice 
attack  tones?  (3)  Are  the  fluctuations  of  the  voice  such  that  give 
proof  of  control  by  the  ear?  (4)  How  many  stress  degrees  of 
muscular  tetanus  are  we  justified  in  accepting  through  the  perform- 
ance of  the  muscles  of  the  larynx? 

Kliinder  found  that  for  the  pitches  96,  128,  192,  256,  v.d.,  respect- 
ively, he  himself  as  observer  made  the  following  ±  errors :  .32  v.d.,^ 
.47  v.d.,  .62  v.d.,  and  .59  v.d.  This  however  was  somewhat  better 
than  any  of  his  other  observers  could  do. 

From  this  Kliinder  concludes  that  the  voice  is  very  accurate  in 
reproduction  of  pitch  and  he  answers  his  questions  in  substance  as 
follows : 

■Previous  to  this  time  Scott  (17)  and  Blake  (3)  had  developed  phonauto- 
graphs for  registering  voice  curves. 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  15 

(i )  The  vocal  cords  are  held  in  labial  tension  by  muscular  tetanus. 
(2)  The  musculature  allows  from  40  to  170  different  tensions  in  the 
tetanus.  (3)  The  regulation  of  the  pitch  of  the  voice  takes  place 
directly  through  the  sensation  of  tension  in  the  larynx. 

Seashore  (19)  in  1910  published  in  a  very  condensed  form  the 
results  of  experiments  carried  on  in  1905  by  himself  and  E.  A. 
Jenner.  Previous  to  that  time,  however,  much  work  had  been  done 
in  perfecting  a  registering  apparatus,  the  tonoscope,  which  is  fully  de- 
scribed by  Professor  Seashore  in  the  foregoing  article  in  this  volume 
of  the  Studies.  Some  preliminary  experimenting  also  was  done  in 
1 90 1 -'02  with  the  help  of  Edward  Bechly,  the  results  of  which  have 
never  been  published.  Seashore  and  Jenner  in  their  work  sought  to 
answer  two  questions  :  ( i )  Can  we  facilitate  development  of  control 
in  the  pitch  of  the  voice  by  using  an  aid  to  the  ear  in  training? 
(2)  May  the  ordinary  limits  of  accuracy  be  exceeded  by  training 
with  such  an  aid?  In  attacking  these  problems  they  used  three 
measurements:  (i)  accuracy  in  reproducing  a  given  tone,  (2)  ac- 
curacy in  singing  a  required  interval,  and  (3)  the  least  producible 
change  in  the  pitch  of  the  voice.  The  standard  or  fundamental 
tone  was  100  v.d.,  produced  by  a  large  tuning-fork ;  the  intervals 
were  the  major  third,  the  fifth,  and  the  octave  above  this.  The 
least  producible  change  was  determined  for  each  of  these  four  tones 
(i)  in  the  least  producible  sharp  and  (2)  in  the  least  producible 
flat  from  the  note  as  actually  sung.  Each  period  of  practice  con- 
sisted of  one  hundred  and  sixty  trials,  which  took  about  forty-five 
minutes.  The  tests  continued  twelve  days,  approximately  succes- 
sive. During  the  first  five  days  the  singer  depended  entirely  on  the 
ear  as  in  ordinary  singing:  then  followed  five  days  of  singing  with 
aid,  i.e.,  the  observer  was  informed  of  the  result  of  each  trial  imme- 
diately after  it  was  made.  The  records  of  the  eleventh  day  were 
taken  without  aid,  while  on  the  twelfth  day  aid  was  again  given. 
Six  men  acted  as  observers.  The  conclusions  of  this  investigation 
are  quoted  as  follows: 

"(i).  The  aid  enhances  the  ability  to  strike  a  tone  which  has 
been  heard.  The  superiority  of  the  aided  series  over  the  unaided 
amounts  to  42  per  cent.  (2)  The  aid  enhances  the  ability  to  sing 
an  interval.  The  superiority  of  the  aided  series  over  the  unaided 
amounts  to  50  per  cent,  for  the  major  third,  50  per  cent,  for  the 
fifth,  and  60  per  cent,  for  the  octave.     (3)  The  voluntary  control 


i6  WALTER  R.  MILES 

of  the  pitch  of  the  voice  is  improved  by  the  aid.  The  average 
superiority  of  the  aided  series  over  the  unaided  for  all  intervals 
amounts  to  26  per  cent.  (4)  There  is  probably  some  transfer  of 
gain  from  the  aided  training  to  following  unaided  singing.  (5)' 
There  is  no  evidence  of  transfer  of  the  gain  in  the  accuracy  of  the 
memory  image.  This  is  undoubtedly  due  to  the  fact  we  have  here 
to  do  with  memory  rather  than  discrimination  and  the  acquisition 
of  accurate  memory  images  is  a  slow  process — too  slow  in  this 
short  series.  (6)  The  gain  in  the  discriminative  control  of  pitch 
of  the  voice  is  fully  transferred.  (7)  Improvements  in  the  ability 
to  sing  a  tone  or  an  interval,  and  the  ability  to  produce  a  minimal 
change,  are  very  much  more  pronounced  and  more  rapid  in  the 
aided  than  in  the  unaided  series.  (8)  The  second  question  is  not 
answered  absolutely  by  our  records,  but  it  seems  probable  (a)  from 
the  radical  and  immediate  improvement  of  the  aided  series  over  the 
unaided,  and,  (b)  from  the  introspection  showing  a  tone  which 
without  the  instrument  seemed  entirely  satisfactory  to  the  ear  could 
be  corrected  by  the  ear  after  the  error  had  been  pointed  out  by  the 
instrument,  that  a  higher  degree  of  accuracy  of  pitch  in  singing 
may  be  attained  by  aiding  the  ear  in  the  training  than  would  be  pos- 
sible to  attain  without  such  aid.  No  matter  how  keen  the  ear  of 
a  trained  musician,  it  can  be  shown  in  a  single  test  that  his  ear  has 
been  "too  generous" — too  easily  satisfied,  for  when  the  error  is 
pointed  out  objectively  he  can  recognize  it.  We  thus  find  cumu- 
lative evidence  to  show  that  the  singer  can  not  reach  the  physio- 
logical limit  of  accuracy  by  the  ordinary  methods  of  voice  culture, 
because  he  has  no  objective  criterion  by  which  he  can  check  up  the 
accuracy  of  his  ear.  (9)  The  major  third,  the  fifth,  and  the  octave 
are  approximately  equally  difficult  intervals  to  sing.  If  we  express 
the  average  error  in  relative  fractions  of  a  tone  (  1/25  of  a  tone) 
instead  of  in  vibrations,  the  ratio  is  1.4,  1.5,  and  1.4,  for  the  three 
intervals  named  above.  The  average  error  expressed  in  terms  of 
vibrations  shows  that  the  difficulty  of  a  natural  interval  varies  ap- 
proximately with  the  magnitude  of  the  interval.  (10)  The  minimal 
change  is  a  relatively  constant  fraction  of  a  tone  within  the  octave. 
This  is  true  for  both  the  aided  and  the  unaided  series.  If  we 
reduce  the  records  from  vibrations  to  twenty-fifths  of  a  tone,  the 
minimal  change  is  3.1,  3.1,  3.6,  2-3,  for  the  fundamental,  the  major 
third,   the  fifth,  and  the  octave   respectively.     This  is   surprising, 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  17 

because  within  this  part  of  the  tonal  range  the  pitch  discrimination 
is  normally  measured  by  a  constant  vibration  frequency  instead  of 
by  a  constant  part  of  a  tone." 

Cameron  (4)  1907,  varied  somewhat  the  conditions  of  the  ex- 
periment as  performed  by  Kliinder.  In  the  first  series  the  subject 
was  asked  to  sing  any  tone  of  medium  pitch,  a  second  tone  of  low 
pitch,  and  a  third  of  high  pitch,  and  to  sustain  the  pitch  selected 
in  each  case  as  uniformly  as  possible  throughout  the  singing.  The 
second  series  was  like  the  first  except  that  each  tone  was  inter- 
rupted by  the  insertion  of  short  pauses  of  .3  second  duration.  In 
a  third  series,  somewhat  longer  than  those  previously  mentioned, 
the  ability  of  one  observer  to  imitate  organ  tones  in  the  range  94 
v.d.  to  303  v.d.  was  tested.  The  tones  were  reproduced  in  sequence 
and,  in  chance  order,  partly  simultaneously  with  the  standards  and 
partly  by  singing  the  tones  immediately  after  the  organ  had  ceased 
sounding.  In  a  fourth  series  various  distracting  tones,  (i)  harmo- 
nious or  inharmonious  with  the  standard  tone;  (2)  of  greater  or  less 
interval  from  the  standard;  and  (3)  higher  or  lower  than  the 
.standard,  were  introduced  either  at  the  beginning  or  just  preceding 
the  beginning  of  the  reproduction  by  the  observer.  The  more  im- 
portant results  of  the  study  are  here  summarized : 

"(i)  In  the  singing  of  a  tone  a  sudden  marked  rise  in  pitch 
usually  occurs  near  the  beginning  of  the  tone.  This  rise  in  pitch 
is  so  general  as  to  seem  to  indicate  a  universal  tendency.  (2)  No 
tone  is  sung  entirely  uniformly.  It  oscillates  in  pitch  from  period 
to  period  throughout  its  length  in  a  somewhat  irregular  rhythmical 
fashion.  (3)  Very  marked  differences  exist  in  different  individuals 
with  regard  to  their  ability  to  imitate  a  standard  tone.  The  subjects 
tested  varied  in  degrees  of  accuracy  in  imitation  of  standard  tones  of 
different  pitch  from  a  small  fraction  of  i  per  cent,  to  13  per  cent, 
of  error.  (4)  There  is  manifest  throughout  a  tendency  to  sing 
a  tone  higher  than  it  should  be  sung.  Thus  the  end  of  a  tone  is 
usually  higher  than  the  beginning  and  the  sung  tone  (as  a  whole) 
is  almost  invariably  Higher  than  the  standard  tone.  (5)  Distrac- 
tions when  causing  disturbances  may  affect  the  whole  of  the  sung 
tone  or  only  the  beginning  of  the  tone.  In  either  case  the  effect  of 
the  distraction  may  be  to  cause  the  sung  tone  to  vary  from  the 
standard  (a)  in  the  direction  of  the  distracting  tone;  or  (b)  in  the 
opposite  direction  from  the  distracting  tone.     (6)  Sung  tones  vary- 


i8  WALTER  R.  MILES 

ing  from  the  standard  under  the  effect  or  distraction  are  usually 
harmonious  with  the  distracting  tone.  When  the  distracting  tone 
is  inharmonious  with  the  standard  tone,  distraction  is  more  likely 
to  occur  than  when  the  two  tones  form  a  harmony.  (7)  A  person 
may  more  or  less  closely  imitate  a  tone  which  he  has  heard  when  his 
attention  was  engrossed  in  singing  another  tone  of  a  standard  pitch." 

An  important  contribution  to  the  general  problem  of  control  of 
the  pitch  of  the  voice  in  singing  was  made  by  Berlage  (2)  in  1910. 
During  the  summer  of  1907  Berlage  carried  on  a  series  of  experi- 
ments in  which  definite  time  intervals  were  inserted  between  the 
breaking  off  of  the  standard  tone  and  the  beginning  of  the  reproduc- 
tion by  the  observer.^  These  intervals  were  of  the  following 
values  stated  in  seconds:  i,  2,  3,  4,  5,  7,  10,  15,  20,  25,  and  30.' 
The  tones  were  all  sounded  as  "a"  ('a'  in  *ah').  This  series  is 
an  amplification  of  the  methods  of  Kliinder  and  Cameron,  and  was 
undej-taken  for  the  purpose  of  finding  the  time  interval  most  favor- 
able for  the  imitation  of  tones,  which  when  found  became  one  of 
■the  conditions  of  further  experimentation. 

In  the  winter  of  i907-'o8  Berlage's  general  problem  was  to  de- 
termine the  influence  of  articulation  and  hearing  in  the  vocal  repro- 
duction of  tones.  In  this  series  (second)  as  in  the  third  series  by 
Berlage  the  standard  tones  to  be  imitated  are  voice  tones.  The 
variation  of  conditions  consisted  in  having  the  standard  tones  sung 
part  of  the  time  by  the  observer  and  part  of  the  time  by  the  experi- 
menter thus  showing  the  immediate  influence  of  hearing  and  of  loud 
articulation  in  tone-reproduction.  It  seemed  desirable  to  determine 
to  what  extent  the  influence  of  articulation  is  due  to  the  larynx,  and 
to  the  mouth  cavity.  For  this  purpose,  in  a  third  series  of  experi- 
ments, all  the  standard  tones  were  sung  by  the  observers,  the 
vowel  quality  being  varied  under  control.  The  standard  and  repro- 
duction were  sung,  sometimes  to  the  same  vowel  as  "i",  "i" ,  or 
"u",  "u",  and  at  other  times  to  different  vowels  as  to  "i",  and  "u" 
or  "a"  and  "u".  The  chief  conclusions  reached  from  Berlage's 
experiments  are  the  following: 

(i)  "Accuracy  in  the  reproduction  of  a  "strange"  voice  tone 
decreases  rather  regularly  with  the  increasing  time  interval  of 
from  I  to  30  seconds.    Accuracy  is  greatest  with  an  interval  of  from 

'  Berlage  designates  these  tones  as  'foretone'  and   'aftertone'.     'Standard' 
and   'reproduction'   are   used    throughout   this    study. 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  19 

I  to  2  seconds.  The  values  found  here,  for  the  variable 
average  error,  in  the  case  of  the  observers  amounted  to  only  .5  v.d, 
and  .6  v.d.  (2)  Observers  reproduced  their  own  voice  tones  more 
accurately  than  those  of  another  (time  interval  3  seconds).  (3) 
The  increase  of  precision  shows  itself  chiefly  in  a  decrease  of  the 
constant  error.  In  the  reproduction  of  outside  standards  and  es- 
pecially when  they  are  near  the  boundaries  of  the  voice  range  there 
is  a  tendency  toward  a  constant  error  near  the  middle  of  the  voice 
range.  (4)  In  the  reproduction  of  one's  own  tones  vowel  change 
works  a  disadvantage  upon  precision.  With  the  standard  tone  sung  as 
"u"  and  the  reproduction  as  "i"  there  is  a  tendency  for  the  latter 
to  be  lower,  and  vice  versa  when  the  vowels  are  changed.  (5)  In 
the  reproduction  of  an  outside  standard  the  variable  average  error 
expressed  in  vibration  frequency  becomes  larger  with  rising  pitch, 
while  if  expressed  in  per  cent,  of  vibration  frequency  it  diminishes. 
(6)  In  the  reproduction  of  one's  own  tones  the  variable  average 
error  expressed  in  vibration  frequency  remains  rather  constant  with 
rising  pitch.  (7)  The  amount  of  departure  of  the  individual  tone 
sections  (measured  off  in  .1  second  periods)  from  the  general 
average  of  the  reproduction  shows  no  tendency,  in  the  variations 
carried  out  in  these  experiments,  to  change  according  to  the  ordinal 
number  of  the  tone  sections  in  the  course.  (8)  Only  in  the  first 
.1  second  is  the  reproduction  regularly  lower  than  the  rest  of  the 
tone  course.  (9)  Reproductions  after  the  time  intervals  of  from 
3  to  10  seconds,  in  the  case  of  two  observers,  show  a  sudden  raising 
or  lowering  of  the  tone  after  the  tone  has  progressed  some  .4 
to  1.2  seconds.  (10)  The  average  departure  of  individual  tone 
sections  from  the  average  for  the  tone  is  greatest  in  the  repro- 
duction of  one's  own  tones.  (11)  The  total  amount  of  departure, 
expressed  in  vibration  frequency  grows  with  rising  pitch  so  that — 
not  considering  rather  marked  irregularities  with  the  individual 
observers — the  amount  of  variation  expressed  in  per  cent,  of  a 
tone  remains  about  constant." 

The  latest  published  study  of  this  general  problem  to  come  to 
our  attention  is  that  of  Sokolotvsky  (22)  191 1.  His  apparatus  con- 
sisted of  a  combination  of  the  Einthovan  string-galvanometer  and 
the  Weiss  phonoscope.  The  organ  tones,  which  were  used  for 
standards,  acted  on  the  string-galvanometer  and  the  sung  tones  on 
the  phonoscope.  Both  tones  were  registered  in  a  convenient  way 
for  comparison  by  means  of  the  Blix-Sandstrom  photokymograph. 


20 


WALTER  R.  MILES 


Sokolowsky  secured  the  cooperation  of  seven  professional  opera 
singers,  three  men  and  four  women.  The  observers  w^ere  allowed  to 
choose  the  vowel  to  which  they  sang  the  tones.  The  musical  "a" 
was  chosen  most  frequently.  There  were  three  short  series  of  ex- 
periments :  ( I )  singing  a  given  tone  simultaneously  with  the 
sounding  of  the  tone  by  the  organ  (unison)  ;  (2)  allowing  a  time 
interval  between  the  organ  tone  and  its  reproduction.  (The  inter- 
vals used  were  30,  60,  and  120  seconds,  during  which  the  observers 
were  instructed  not  to  hum  or  sing  to  themselves)  ;  and  (3)  singing 
a  specified  interval  from  a  simultaneously  sounding  organ  tone.  The 
musical  intervals  selected  were  the  third,  fourth,  fifth,  sixth  and 
octave. 

The  results  from  these  three  series  of  experiments  may  be  sum- 
marized as  follows :  ( i )  Curves  for  8  tones  were  secured  in  series 
I.  The  average  pitch  was  251  v.d.  (range  165  to  296  v.d.),  the 
average  error  was  ±  0.44  per  cent.  The  average  pitches  for  men 
and  women  respectively  were  197  and  286  v.d.,  with  average  ± 
errors  of  0.51  and  0.40  per  cent.  (2)  The  introduction  of  a  time 
interval  increases  the  average  error  to  ±  0.99  per  cent,  as  compared 
with  ±  0.44  of  the  previous  series.  Errors  are  usually  larger  with 
an  interval  of  60  seconds  than  with  30  seconds.  (3)  The  average 
error  in  series  III  is  ±  1.51  per  cent.  The  largest  errors,  average 
dr  3.28  per  cent,  are  on  the  fifth,  while  the  smallest,  average 
±  0.78  per  cent,  are  on  the  third.  (4)  Of  the  entire  number  of  tones 
counted  (46)  36  are  sung  flat  and  10  sharp.  The  errors  on  the  side 
of  sharping  are  divided  among  three  women  and  one  man ;  those  on 
the  side  of  flatting  between  three  men  and  three  women. 

Giittmann  (6)  1912,  in  his  consideration  of  the  psychophysics  of 
singing  gives  some  attention  to  the  problem  of  accuracy  in  reproduc- 
ing pitch  and  states  that  recently  he  has  been  engaged  in  an 
extensive  research  in  this  field.  The  results  are  to  be  published 
shortly  in  one  of  the  psychological  journals,  but  in  a  preliminary 
way  he  says  that  they  agree  in  general  with  those  secured  by 
Kliinder  and  Sokolowsky,  but  he  thinks  that  the  results  of  the 
latter  (unison  curves)  are  "too  good". 

Other  investigators,  among  them  Hensen  (10)  and  more  recently 
Marbe  (14),  Griitsner  (5)  and  Scripture  (18)  have  developed 
methods  for  recording  the  pitch  of  the  voice,  but  these  seem  not  to 
ha,ve  been  used  in  gathering  data  on  our  problem. 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  21 

THE  TONOSCOPE 

In  the  investigations  of  Kliinder,  Cameron  and  Berlage  the 
vibration  frequency  of  the  tones  was  recorded  in  tracings  on  smoked 
paper.  Sokolowsky  photographed  his  records ;  after  these  had  been 
rendered  permanent  the  waves  were  counted  and  the  pitch  deter- 
mined by  comparison  with  a  time  or  standard  hne.  This  method, 
commonly  known  as  "graphic  recording"  has  been  used  with  various 
refinements  by  many  investigators  in  the  field  of  phonetics.  While 
reliable,  it  is  at  best  indirect  and  very  laborious. 

Seashore  and  Jenner  in  their  research  made  use  of  an  early  model 
(20)  of  the  tonoscope.  This  instrument  as  lately  improved  was 
used  by  the  author  in  the  present  experiments.*  It  has  several 
advantages  which  recommended  it  as  an  instrument  for  the  measure- 
ment of  the  pitch  of  tones.  In  the  first  place  readings  are  made 
quickly  and  directly.  The  instant  a  tone  is  sounded  the  vibration  fre- 
quency is  indicated  by  a  row  of  dots.  The  experimenter  has  simply 
to  note  the  number  of  this  row  and  to  record  it.  He  is,  therefore, 
enabled  to  secure  a  large  number  of  observations  in  a  relatively  short 
time.  It  is  not  difficult  to  take  two  hundred  records  in  thirty  minutes. 
In  the  second  place  the  experimenter  has  the  advantage  of  knowing 
how  the  test  is  progressing.  If  a  preliminary  practice  series  is  de- 
sired to  acquaint  the  observer  with  some  procedure  we  have  in  the 
direct  readings  from  the  tonoscope  an  index  to  the  observer's  un- 
derstanding of  the  test.  The  observer  must  be  kept  actively  trying 
throughout  the  experiment.  In  psychological  tests,  such  as  the 
imitation  of  tones  by  singing,  there  is  so  much  repetition  in  the  pro- 
gram for  the  observer  that  his  attention  easily  wanders.  Large 
and  unnatural  errors  are  therefore  likely  to  be  found  in  the  records. 
Here  the  tonoscope  as  a  recording  instrument  has  an  advantage 
over  other  methods  as  it  provides  for  detecting  these  errors  as 
soon  as  they  occur.  The  experimenter  as  he  takes  each  reading 
notes  roughly  the  attack,  the  steadiness,  and  the  degree  of  success 
with  which  the  reproduction  approaches  the  standard.  He  thus  easily 
becomes  acquainted  with  the  unusual  range  of  variability  and  forms 
an  estimate  of  the  observer's  power  to  control  his  voice.    When  a 

*  The  instrument  is  fully  described  in  the  preceding  article  in  this  volume 
of  Studies,  "The  Tonoscope",  by  Professor  Seashore.  A  reading  of  that 
article  is  essential  for  an  understanding  of  the  present  report. 


22  WALTER  R.  MILES 

tone  of  unusual  divirgence  is  given  he  therefore  immediately  recog- 
nizes it  and  can  take  cognizance  of  it,  asking  for  introspection  or  for 
a  new  trial,  and  all  with  scarcely  any  loss  of  time.  He  may  thus 
check  up  and  to  some  extent  control  the  observer, — keep  him  at 
his  best.  Furthermore  the  possibility  of  encouraging  the  observer 
or  even  of  giving  him  full  information  regarding  the  success  or 
failure  of  each  trial  is  in  itself  a  most  important  asset. 

The  tonoscope  has  been  criticised  as  giving  only  an  approximate 
result,  because  the  pitch  of  the  singing  voice  is  not  uniform  and  it 
is  therefore  necessary  in  reading  the  instrument  to  select  the  pre- 
dominating pitch.  This  criticism  stands  or  falls  according  to 
the  needs  of  the  problem  to  be  attacked.  If  one  were  studying  the 
oscillations  of  the  voice,  or  the  variations  of  the  individual  sections 
of  a  tone,  as  for  example  the  difference  in  pitch  between  the  first 
tenth  and  the  fifth  tenth  of  a  second  of  a  tone,  it  would  be  better  to 
use  a  graphic  method.  But  even  in  such  problems  as  these  the 
tonoscope  is  not  without  its  possibilities.  The  characteristics  of 
tonal  attack  in  singing  are  easily  discernible  in  the  configurations 
on  the  screen.  With  many  of  the  problems  which  lie  in  our  field 
there  is  no  need  for  so  detailed  a  record.  The  predominant  or 
modal  pitch  of  a  tone  of  from  one  to  two  seconds  in  length  is  all 
that  is  needed  for  much  of  the  work  in  the  psychology  of  pitch 
singing.  The  tonoscope  can  of  course  meet  this  condition  admir- 
ably, as  it  is  this  modal  pitch  which  stands  out  clear  and  distinct, 
forcing  itself  upon  the  attention  of  the  experimenter. 

Tonoscope  reading  test. — The  method  of  reading  the  tonoscope, 
and  the  various  sources  of  error  having  been  fully  treated  by  Pro- 
fessor Seashore  in  the  accompanying  article,  there  is  no  need  to 
repeat  them  here. 

In  order  to  determine  the  degree  of  accuracy  in  the  reading  of 
the  tonoscope  the  following  experiment  was  performed.  A  set  of 
ten  large,  movable-disc,  tuning  forks  ranging  from  128  to  131  v.d. 
was  so  tuned  that  no  two  forks  had  a  pitch  difference  of  over  3  v.d. 
and  in  the  great  majority  of  cases  the  differences  were  much 
smaller.  A  revolving  shutter,  rotated  by  the  tonoscope  shaft,  was 
so  arranged  as  to  expose  the  mouth  of  a  resonator  connected  with 
the  sensitive  light  for  the  following  time  intervals :  .25,  .50,  .75  and 
1. 00  second.  In  this  way  a  tone  sounded  before  the  shutter  was 
registered  by  the  tonoscope  for  just  the  period  during  which  the 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  23 

resonator  was  exposed.^  The  presentation  of  the  tones  and  the 
recording  of  the  observations  were  in  charge  of  two  helpers.  The 
experimenter  did  nothing  but  watch  the  moving  screen  and  call  out 
the  readings.  He  had  no  way  of  knowing  the  real  reading  in  any 
case.  Five  trials  were  given  on  each  fork  with  each  exposure 
interval.  The  order  of  the  forks  was  determined  approximately  by 
chance.    There  was  an  interval  of  about  five  seconds  between  tones. 

After  the  fifty  trials  with  the  .75  second  exposures  were  finished, 
the  pitch  of  each  fork  was  carefully  determined  with  the  tonoscope, 
counts  being  made  by  the  stop-watch  during  periods  of  from  6  to 
15  seconds.  These  records  formed  the  basis  from  which  to  compute 
the  errors  in  the  first  test.  The  assistant  then  changed  the  pitch  of 
all  the  forks  and  the  above  procedure  was  repeated  with  a  .50 
second  exposure.  Again  the  forks  were  changed  and  the  same  pro- 
cedure was  followed  for  the  i.oo  second  and  the  .25  second  expos- 
ures in  turn.  Thus  fifty  records  v/ere  obtained  for  each  of  the  four 
exposure  periods  and  the  conditions  were  such  that  the  reader  could 
have  no  accessory  clue.    The  record  is  summarized  in  Table  I. 

To  test  the  reading  ability  for  tones  one  octave  higher,  i.e. 
256  v.d.,  where  it  will  be  recalled  the  tonoscope  reading,  and  hence 
the  errors,  must  be  doubled,  a  set  of  seven  small  forks  was  pro- 
vided. These  were  weighted  so  that  no  pitch  difference  between  any 
two  forks  was  greater  than  3  v.d.  The  test  was  made  with  the 
exposure  interval  of  .75  second. 

In  making  the  pitch  difference  between  the  forks  come  within 
a  range  of  3  v.d.  we  approximate  the  condition  presented  when 
working  with  voice  tones  that  require  accuracy  in  reading.  If  an 
observer  is  asked  to  reproduce  a  tone  or  to  sing  an  interval  the 
experimenter  knows  approximately  the  point  on  the  scale  where  the 
reading  should  occur.  He  is  watching  this  point.  Should  the 
reproduction  be  nearly  correct  and  the  tone  fairly  constant  for,  say 
.50  second,  he  can  read  according  to  our  result  (see  Table  I)  within 
an  error  of  less  than  ±  .2  v.d.  If  however  the  reproduction  goes 
wide  of  the  mark,  for  example  to  the  extent  of  6  v.d.  there  is  no 
need  of  reading  in  fractions  smaller  than  halves. 

"  This  arrangement  is  not  ideal  in  that,  as  the  tone  is  turned  on  and  cut  off 
by  the  disc,  slightly  disturbing  waves  are  set  up  and  show  on  the  screen. 
In  test  No.  4  where  the  tone  sounded  for  .25  second  this  was  felt  to  be  very 
disturbing.  The  real  time  given  for  the  reading  of  the  tones  in  all  these 
tests  was  thus  slightly  less  than  that  represented  by  the  several  discs. 


.12 

v.d.     , 

m.v. 

.lO 

V.( 

•15 

a 

a 

.12 

u 

.19 

li 

a 

.17 

t( 

.18 

a 

.       ** 

.11 

(( 

.65 

ti 

a 

.27 

a 

24  WALTER  R.  MILES 

TABLE  L      The  degree  of  accuracy  in  the  reading  of  the  tonoscope 

Exposure  i.oo  sec.  Ave.     error 

.75    "  (128  v.d.) 

.75    "  (256  v.d.) 

.50    "  (128  v.d.) 

.25    "  (128  v.d.) 

EXPERIMENTS  SERIES  I:     ACCURACY  AND  THE 

VOICE  RANGE 

In  the  first  five  series  of  experiments  the  purpose  was  to  answer 
questions  concerning  some  factors  which  must  be  considered  in  any- 
adequate  test  of  voice  control,  (i)  How  does  accuracy  of  control 
vary  with  the  range  of  the  voice?  (2)  How  does  the  intensity  of 
the  standard  tone  affect  the  pitch  reproduction?  (3)  What  is  the 
relation  of  voice  volume  to  voice  control?  (4)  Are  the  reproduc- 
tions aifected  by  the  timbre  of  the  standard  tones?  (5)  Do  vowel 
changes  (timbre  changes)  in  the  reproductions  cause  changes  in 
the  pitch  of  the  reproduction?  The  sixth  series  represents  an 
effort  to  combine  into  a  single  test  the  results  of  our  previous  ex- 
periments, together  with  those  of  other  investigators,  and  to  give 
this  test  to  a  sufficiently  large  group  that  we  might  be  enabled  to 
determine  from  the  results  some  of  the  norms  of  voice  control.*' 

Seventeen  men  with  splendid  enthusiasm  gave  their  services  as 
observers  in  the  experiments  of  Series  I.  From  among  this  number 
several  were  selected  to  serve  as  observers  in  Series  II,  III,  IV, 
and  V.  The  observers  were  all  of  mature  age  and  more  than  half 
their  number  had  had  some  training  in  the  methods  of  experimental 
psychology.  P,  the  only  professional  musician  in  the  group,  is  a 
teacher  of  "Voice"  and  a  thoroughly  trained  tenor  soloist.  H,  a 
baritone  of  extensive  special  training,  has  for  some  time  been  the 
leader  of  a  large  choir.  He  is  a  soloist  of  ability.  Ma.,  W,  and 
V.  Z.  have  all  had  special  training  in  singing,  and  much  experience 
in  solo,  quartette  and  glee  club  work.  S,  C.  Mi.,  Ro.,  An.,  Wi., 
and  V.  H.  all  have  had  considerable  experience  in  general  singing 
but  are  without  special  training.  Ri.,  Ab.,  Mc,  Br.,  D,  and  Bh. 
very  seldom  sing  in  public  but  they  enjoy  music. 

'Gutzmann  (7)  and  Sokolowsky  (22)  suggest  some  of  the  above  problems, 
especially  Nos.  i  and  5  as  being  important.  These  articles  and  suggestions 
however  did  not  come  to  the  attention  of  the  writer  until  the  experimentation 
was   completed. 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  25 

For  Series  I  the  standard  tones  were  provided  by  a  set  of  twenty 
tuning  forks  tanging  approximately  by  the  chromatic  scale  from 
Q,  64  v.d.,  to  and  including  a',  426  v.d.  The  first  fourteen  forks 
beginning  with  64  v.d.  were  large  and  carried  discs.  All  the  tones 
were  of  good  quality  and  their  duration  of  tone  was  more  than 
ample.  Some  of  the  forks  were  of  different  vibration  frequency 
than  that  indicated  by  the  notes  of  the  chromatic  scale ;  for  example, 
the  pitch  of  the  fork  that  corresponded  to  G  was  182  v.d.  in  place  of 
192  v.d.  These  differences  were  made  in  order  to  check  the  ob- 
servers from  judging  and  singing  the  various  steps  as  musical 
intervals. 

An  independent  selection  of  five  forks  was  made  for  each  ob- 
server after  a  preliminary  determination  of  his  voice  range.  These 
forks  covered  approximately  one  and  one-half  octaves  in  the  middle 
of  the  range  and  were  fairly  distributed.  In  giving  the  test  the 
experimenter  presented  the  tones  to  the  ear  of  the  observer,  who, 
after  listening  for  1.5  seconds  and  allow-ing  a  time  interval  of  i 
second,  reproduced  the  pitch  of  the  tones  as  accurately  as  possible. 
Proceeding  from  the  lowest  to  the  highest  and  then  in  reverse  order 
back  to  the  lowest,  each  tone  was  given  twice  in  succession,  the  test 
consisting  of  twenty  trials  on  each  standard  tone. 

The  results  of  these  experiments  are  present  in  Table  II.  O 
denotes  the  observer ;  P,  the  pitch  of  the  standard  tone ;  E,  average 
error;  m.v.,  mean  variation;  and  C.E.,  constant  error.  These  five 
successive  columns  give  the  record  of  the  respective  standards  for 
each  observer.  The  footings  in  the  table  show  the  averages  of  the 
figures  above  stated,  first  in  terms  of  vibration  (absolute)  and 
second,  in  terms  of  percentage  of  a  tone  (relative)  at  the  respective 
levels.  The  average  C.  E.  in  the  footing  is  the  average  of  C.  E. 
regardless  of  sign;  in  the  second  the  sign  is  taken  into  account 
giving  group  tendency  of  the  constant  error,  or  group  constant 
error  (G.  C.  E.).  These  footings  are  represented  graphically  in 
Fig.  I. 

Taken  as  a  whole  these  records  show  that  accuracy  in  the  repro* 
duction  of  the  pitch  of  a  tone,  as  measured  by  the  average  error 
(E)  with  its  mean  variation  (m.v.)  the  average  of  the  constant 
errors  (C.  E.)  and  the  general  tendency  of  the  constant  errors 
(G.  C.E.),  tends  to  be  a  constant  in  terms  of  vibration  frequency. 
This  is  shown  in  Fig.  i   (A)  by  the  fact  that  the  four  curves,  for 


26  WALTER  R.  MILES 

the  absolute  variation  tend  to  remain  horizontal  lines  whereas  the 
four  curves  for  the  relative  variation  (B)  tend  to  fall  in  inverse 
ratio  to  the  rise  of  the  pitch.  The  slight  tendency  to  deviate  from 
the  constant  in  terms  of  vibrations  is  in  the  direction  of  decrease  in 
accuracy  with  rising  pitch.     This,  in  the  case  of  the  highest  tone, 

TABLE  n.     Accuracy  and  the  voice  range 
E. 
O        P         m.v.       P 
C.E. 
1.6 
P.      128  I.I       160 

—1.5 

1.4 
H.        95  .6      120 

+  14 

i-S 

Ma.        95  -7       120 

—1.5 

•9 
W.      120  .9      144 

+   .2 
3.1 

V.Z.      120         I.I      144 

+3.1 

2.6 

S.      120  .8      144 

—2.4 

•9 

C.        95  1-2      144 

+  .2 
2.9 
Mi.        86         2.3      120 

+4.0 

2.3 

Ro.        95  4-5       144 

+  .1 

5.0 
An.        95  2.3       120 

+Z-7 

3-5 
V.H.      107  1.7      128 

+2.7 

2.3 
Ri.        95  1-9       144 

+2.5 


E. 

E. 

E. 

E. 

m.v. 
C.E. 

P 

m.v. 
C.E. 

P 

m.v. 
C.E. 

P 

m.v. 
C.E. 

1.2 

.6 

— 1.2 

182 

.9 
.8 

+  .4 

256 

1.9 

1.6 

—1.6 

320 

1.2 
1.2 

+  .4 

3.1 
I.I 

+3-1 

160 

.7 

.7 

—  .1 

213 

2.9 

14 
—2.9 

286 

2-7 
1.4 

—2-7 

.8 

.8 

+  4 

160 

3.0 
I.I 

+2.9 

240 

3.7 

1.0 

+Z.7 

286 

3.1 

1-3 

+3-0 

1.0 

.8 

+  .4 

182 

1.7 

1.6 

—  .2 

256 

2.5 

1.5 

+1.9 

320 

1.8 

1.7 
—  .1 

1.6 

.7 
+  1.6 

182 

1.7 
.9 

+  14 

256 

I.I 
I.I 

+  •3 

341 

2.7 

1.4 
+1.7 

1.8 
.9 

— i.S 

182 

1.0 

.8 
—  .3 

240 

2.1 

1.2 

—  .9 

286 

7.1 
1.8 

+7.1 

.7 
■7 

—  .0 

I.I 

.8 

+1.0 

182 
182 

.8 

.6 

—  .3 

1.6 

1-9 

—  .1 

256 

256 

1-3 
1.9 

+  .8 
2.7 
2.7 

+  1.0 

341 

341 

17 

1.5 

—  .9 

3.5 

1.8 

+34 

2.9 
2.2 

+2.5 

182 

2.1 
2.0 

+  1.3 

240 

4.5 
1.8 

+4.3 

320 

2.5 
2.0 

+  .2 

1.6 

1-5 
+  -8 

160 

2.5 

2.8 

— 1.0 

213 

4.5 

2.6 

—4.1 

256 

4.6 

3-5 

—3-1 

4.2 

1.4 

-3.6 

160 

2.0 

1-7 
—1.0 

182 

1.2 
1.0 

+  .1 

240 

4.2 
2.2 

+3.9 

2.9 
-1.6 

182 

2.1 
1.9 

+  .2 

240 

4-5 
1-5 

—  .5 

320 

2.5 
2.1 

+2.7 

ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING 


27 


TABLE  II.  (Coiitirmed) 


Ab.        95 


Mc.        95 


Br. 


95 


D.        95 


Bh. 
P 


bc-o 

^  .J 

u    > 

>    G 


120 
103.0 

E 

m.v. 

C.E. 

G.C.E. 


3-2 
i.o 

+3.1 

1-7 

•5 

—1.6 

2.9 

2.2 

+2.7 

1-7 

•9 

—1.4 

1.6 

I.I 

—1-3 


E 
m.v. 


CO 

7.  ^  c     C.E. 
>  (u  -"G.C.E. 


2.3 

1-5 
2.0 

+  .8 

.18 
.11 

.15 

+.06 


128 


120 


144 


128 


144 


5.5 

1.4 

+S.5 

3.9 

1-3 

+3.8 

5.6 
1.0 

+5.2 

3-3 

31 

—  -3 

2.4 

1.6 

+  .9 


135-0 


160 


160 


182 


160 


182 


172.9 


2.6 

1-3 

2.0 

+  1.0 

.15 

.08 

.12 

+.06 


3-1 
•9 

+3.1 

182 

1-3 
.8 

+  1.7 

1.9 

.8 

—1.7 

213 

1.0 

•9 
+  -4 

6.4 

I.I 
+6.4 

256 

3-7 
1.0 

+3.6 

5-9 

2.4 

182 

6.3 
6.6 

—5-9 

—34 

3.0 
I.I 

+3-0 

240 
230.6 

5-1 
1.8 

+S.I 

2.4 
1.3 

1.7 

+  .5 

2.8 
1.8 

2.1 

+  .5 

.11 
.06 

.08 
+.02 

.09 
.06 

•07 
+.02 

256 


256 


384 


256 


286 


1-4 

•9 

+  -9 

2.6 

1.2 
+2.0 

2.7 

2.8 

+1.3 

1 1.2 

5-4 

2.5 

1-4 

+1-5 


299.4 


3-5 
2.0 

2.5 
+  .8 

.10 

•OS 
.06 

+  .02 


'09 


Fig.  I.    Accuracy  and  the  voice  range.     (Table  II) 


is  to  be  accounted  for  mainly  by  the  fact  that  some  observers  were 
erratic  on  this  tone,  probably  because  the  tone  was  higher  than  the 
observer  commonly  sings.  As  a  matter  of  fact  only  half  of  the  ob- 
servers, nearly  all  of  whom  would  be  classed  as  bass  or  baritone  in 
their  range,  show  any  tendency  to  decrease  in  accuracy  at  this 


28  WALTER  R.  MILES 

point;  five  show  the  tendency  to  increase  in  accuracy  and  the  re- 
maining four  tend  to  remain  constant. 

This  result  is  in  harmony  with  results  found  by  Preyer  (i6), 
Luft  (13),  Meyer  (15)  and  Vance  (26)  on  the  sensory  side,  that 
pitch  discrimination  is  approximately  constant  in  terms  of  vibration 
frequency  within  this  range.  It  is  in  harmony  with  the  finding  of 
Berlage  (2)  as  quoted  above:  item  5  (second  part),  that  average 
error  diminishes  with  rising  pitch  if  expressed  in  per  cent,  of  vi- 
bration frequency ;  and  item  6,  with  reference  to  the  reproduction 
of  one's  own  tones. 

It  is  interesting  to  compare  and  to  contrast  these  records  with 
those  of  Seashore  and  Jenner  (19),  item  9,  showing  that  the  average 
error  in  the  singing  of  a  natural  interval  (third,  fifth,  and  octave) 
varies  approximately  with  the  magnitude  of  the  interval;  (see  also 
Sokolowsky's  results  above)  and,  item  10,  showing  that  the  mini- 
mal change  is  a  relatively  constant  fraction  of  a  tone  within  the 
octave. 

The  tendency  for  the  C.  E.  to  be  in  one  direction  (-|-)  will  be 
considered  in  a  later  section  in  connection  with  the  constant  errors 
in  our  other  series  of  experiments. 

EXPERIMENTS  SERIES  II:  INTENSITY  OF  STANDARD 
In  the  experiments  of  Series  I,  as  stated  above,  two  successive 
trials  were  made  on  each  fork.  Occasionally  upon  the  presentation 
of  the  tones  for  the  second  trial  at  reproduction  the  observer  would 
say  ''Let  me  hear  that  again;  it  sounds  higher  (or  lower)  than  be- 
fore", or  "Is  that  the  same  fork?"  Such  remarks  by  careful  ob- 
servers led  to  this  consideration  of  the  intensity  factor. 

The  same  forks  were  used  with  the  respective  observers  as  in 
Series  I.  The  tones  were  presented  to  the  ear  by  the  experimenter 
as  before.  But  with  half  of  the  trials  the  standards  were  made 
about  as  strong  as  possible  by  striking  the  forks  a  heavy  blow  and 
presenting  them  near  the  ear.  The  other  standards  were  made  as 
weak  as  could  be  heard  with  distinctness.  The  observers  were  en- 
couraged to  sing  with  a  medium  volume  of  voice  and  not  to  imitate 
that  of  the  forks,  as  is  the  natural  tendency.  Twenty  records 
were  made  with  each  fork,  ten  on  the  "weak"  and  ten  on  the 
"strong"  in  the  double  fatigue  order,  as  regards  pitch  and  intensity. 
No  successive  trials  were  made  on  the  same  fork  except  on  the 
highest  and  lowest.     Having  sung  the  tones  from  the  highest  the 


ACCURACY   OF   VOICE  IN  SIMPLE  PITCH  SINGING  29. 

observer  would  sing  them  in  reverse  order  from  highest  to  lowest; 
but  a  short  pause  was  introduced  between  such  successive  repro- 
ductions. Of  the  eight  observers  tested,  P,  Ma.,  V.  Z.,  C,  An., 
V.H.,  S  and  Mi.,  the  first  six  had  no  definite  knowledge  of  the 
object  in  view. 

The  results  are  shown  in  Table  III  and  graphically  represented 
in  Fig.  2.  "W"  denotes  weak  and  "S"  strong,  while  the  other 
notation  is  the  same  as  that  previously  used.  It  will  be  seen  that  the 
intensity  of  the  standard  tone  has  a  decided  effect  upon  the  ac- 
curacy of  reproduction. 

(i).  Increase  in  intensity  causes  a  lowering  in  the  pitch  of  the 
reproduction.  The  G.  C.  E.  for  S  on  each  of  the  five  levels  is  less 
than  that  measure  for  W.,  the  minimum  amount  of  difference- 
being  1.4  v.d.,  the  maximum  4.1  v.d.  and  the  average  for  the  five 
pitches,  2.3  v.d.  In  all  the  forty  individual  constant  errors  with  the 
exception  of  two  (see  V.  H.'s  lowest  tone  and  C.'s  highest;  in  this, 
latter  "W."  and  "S/'  are  just  the  same)  the  reproductions  of  the 
"strong"  standards  are  lower  than  those  of  the  "weak".  If  we 
compare  these  averages  (C.  E.'s  and  G.  C.  E.'s)  with  those  of  the 
previous  series  of  experiments  we  find  not  only  that  the  "strong" 
C.  E.'s  and  G.  C.  E.'s  are  lower  in  the  majority  of  cases  than  those 
of  Series  I,  but  that  these  measures  for  the  reproductions  made 
from  the  "weak"  standards  are  somewhat  higher  than  those  of  the 
former  series.  The  effect  of  intensity  in  other  words,  is  evident  in 
both  "weak"  and  "strong"  standards,  the  former  heightening  the 
seeming  natural  tendency  to  sharp  and  the  latter  overcoming  this 
tendency  with  a  more  powerful  one  to  flat.'^ 

(2).  Strong  standard  tones  cause  general  inaccuracy  of  voice  con- 
trol. Most  of  the  observers  stated  that  they  were  less  sure  with  the 
"strong"  standards.  Others  complained  that  the  test  made  their  ears 
tired.  Reference  to  the  mean  variations  and  also  to  the  E.'s  and 
C.  E.'s  will  show  that  in  the  majority  of  cases  these  amounts  are 

^ When  the  conditions  of  this  experiment  (Series  II)  were  explained  to 
P.,  the  professional  musician,  he  remarked  off  hand  as  he  began  the  test : 
"Loud  tones  would  make  your  nerves  more  tense  and  would  in  general  tend 
to  make  you  sharp."  He  was  asked  then  and  at  other  times  during  the  test 
to  let  any  conscious  tendency  to  flat  or  sharp  take  care  of  itself  e.g.  not 
knowingly  to  correct  for  it.  At  the  last  P.  said :  "I  am  equally  satisfied  with 
my  reproductions  of  weak  and  strong.''     Cf.  P.'s  record  in  Table  III. 


30  WALTER  R.  MILES 

TABLE  in.     Intensity  of  standard  tones 
Ave.  P.  105  v.d.  135  v.d.  174  v.d.  237  v.d.  301  v.d. 


W. 

S. 

W. 

S. 

W. 

S. 

W. 

S. 

W. 

S. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

0. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

m.v. 
C.E. 

p. 

1-3 

I.O 

—  •/ 

2.1 

.6 

—2.1 

.7 

.5 

+  -3 

1.2 

■9 
— 1.0 

2.3 

1.2 

+2.3 

1-4 
1.4 

+  -3 

I.I 

.7 
+  1.1 

.7 

•7 

+  .2 

3.0 
1-3 

+2.9 

1.0 

.8 

+  .5 

Ma. 

I.I 

•9 

+1.0 

I.I 
•9 

1.0 
1.0 

—  .2 

1.4 
.8 

—1-4 

3-2 

.8 

+3.2 

1-7 

1-7 

+  .8 

3-1 
.6 

+3.1 

2.1 
1.0 

-)-2.0 

2.1 

■7 
+2.1 

1.4 

1.0 

—1.4 

V.Z. 

3.8 

■7 

+3.8 

1.6 

•9 

+1.2 

2.9 
1.3 

+3.1 

I.I 

•7 
+1.0 

3-2 

.5 
+3.2 

•7 

•7 

1.9 

I -5 

— 1.2 

4.8 

1.2 

-4.8 

2.0 

1.7 
+  -3 

1.8 

1-3 
—2.1 

c. 

1.2 

•5 
+  1.2 

•7 

•7 

+  .2 

1.9 

•5 
+1.9 

I.I 
I.I 

+  .3 

1-7 
.8 

+  1-7 

•7 

■7 

—  .1 

3-0 

I.I 

+3.0 

2.4 

•9 

+2.4 

2.8 
2.0 

+2.6 

2.6 

1.0 

+2.6 

An. 

6.4 

6.4 

+6.4 

5.4 

2.8 

+4.8 

1-9 
1-3 

+  1.9 

I.I 

I.I 

—  .1 

1.9 
1.9 

—  -5 

2.3 

1-3 

—1.9 

3-2 
1.2 

—3.1 

7.8 
1-7 

-7.8 

3-7 
1.8 

—3.4 

8.1 

1.2 

—8.1 

V.H. 

3-1 
1.6 

+2.6 

2.9 

1-7 

+2.9 

3-9 
1.0 

+3.9 

3.5 
1-5 

+2.9 

1.0 
.8 

1-9 

1.8 

— 1.2 

2.2 
1-9 

+  -8 

2.1 

2.1 
+  .3 

2.9 
3.0 

—  .5 

8.0 

3-4 
—8.0 

S. 

1.8 

.5 
—1.8 

4.2 

.7 
—4.2 

1.0 

•5 
+  1.0 

•7 

.6 

—  .4 

.8 

.8 

—  .2 

3.6 

1.0 

-3.6 

2.1 

1.2 

—1.8 

4-7 
.9 

—4-4 

5-3 
1-3 

+5.3 

5-5 

1.4 

+5.5 

Mi. 

9.3 

1.9 

+9.3 

8.5 
4.1 

+8.5 

1-5 
.9 

+  1-5 

1-7 
•9 

+  -5 

2.2 
2.0 

—  .8 

5.4 

2.9 

—5-4 

4.0 

3.1 

+2.4 

4-5 

4.1 

— 2.1 

7.8 
1.9 

+7.8 

4.7 

2.9 

-4.6 

Av.E. 

3-5 

3-3 

1.9 

1.5 

2.0 

2.2 

2.6 

3.6 

3-7 

4.1 

Av.  m.v. 

1-7 

1.6 

•9 

1.0 

I.I 

1.4 

1-4 

1.6 

1.7 

1.6 

Av.  C.E. 

3.4 

3-1 

1.7 

1.0 

1.6 

1-7 

2.1 

3.0 

3-1 

4.1 

G.C.E. 

+2.7 

+  1-3 

+  1.7 

+  .3 

-fi.o 

—1.4 

—  .5 

—1.8 

+2.1 

— 2.0 

larger  with  strong  standards,  thus  indicating  conditions  that  operate 
against  the  best  vocal  control. 

The  matter  of  intensity  has  been  considered  in  the  field  of  pitch 
discrimination,  where  it  must  really  be  worked  out.  Seashore  (21) 
makes  the  following  statements  concerning  it: 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING 


31 


"Extensive  experiments  show  (i)  that  both  trained  and  untrained 
observers  may  be  influenced  by  intensity  in  their  pitch  judgment; 
(2)  that  although  there  is  a  tendency  among  the  untrained,  espec- 
ially the  ignorant,  to  judge  the  loud  tone  the  higher,  it  may  work 
either  way;  (3)  that  the  same  individual  may  show  one  tendency 
at  one  time  and  the  reverse  at  another;  (4)  that  for  trained  ob- 
servers the  two  tendencies  are  about  equal;  and  (5)  that  the 
tendency  is  more  serious  for  large  than  for  small  intensity  differ- 
ences. Introspection  shows  that  this  confusion  rests  largely  on 
motor  tendencies,  or  motor  images.  We  associate  high  and  strong 
with  strain — the  reversal  can  in  some  cases  be  traced  to  a  correc- 
tion, conscious  or  unconscious,  based  on  knowledge  of  this  danger. 

S.S.(3J 

—  7-  /^ 

r;z::.:^-'*^—"im.d(^J 


Fig.  2.     Tne  influence  of  intensity  of  standard  tones. 

"Experiments  show  that  the  just  perfectly  clearly  perceptible  tone 
is  most  favorable  for  accurate  results.  It  is  ordinarily  purer  than 
a  stronger  tone  and  favors  concentration.  Experimenters  must 
guard  against  a  very  common  tendency,  usually  unconscious,  to 
facilitate  the  discrimination  by  making  the  tones  loud ;  and  untrained 
observers  usually  desire  (unwisely)  a  loud  tone." 

These  conclusions  are  found  on  tests  made  by  Anderson  (i)  at 
the  level  of  435  v.d.  Our  results  just  stated  led  to  a  re-examination 
of  the  effect  of  intensity  on  pitch.     Hancock   (8)    found  that  as 


32  WALTER  R.  MILES 

measured  in  terms  of  hearing  alone  the  tendency  to  hear  a  relatively 
low  strong  tone  as  low  is  greater  than  is  shown  in  this  series  for 
singing.  All  these  facts  make  clear  that  in  singing  from  a  standard 
tone  greater  care  must  be  exercised  to  keep  the  tone  constant  and 
at  a  most  favorable  strength.  We  have  no  adequate  quantitative 
data  to  show  what  strength  is  best  but  the  facts  available  tend  to 
support  the  statement  made  by  Seashore  (21)  that  the  just  per- 
fectly clearly  perceptible  tone  is  most  favorable  for  accurate  results.* 


EXPERIMENTS  SERIES  III:     VOLUME  OF  THE  VOICE 

The  effect  produced  by  varying  the  intensity  of  the  standard 
tones  suggested  a  parallel  question  concerning  the  relationship  of 
voice  volume  and  accuracy  of  reproduction.  This  problem  was 
attacked  in  the  following  manner.  The  forks  selected  were  the 
same  for  each  observer  as  in  the  voice  range  test.  Series  I ;  they 
were  presented  to  the  observer's  ear  by  the  experimenter  who 
endeavored  to  keep  the  intensity  as  nearly  constant  as  possible,  and 
the  observer  was  instructed  to  reproduce  the  tones  in  three  degrees 
of  voice  volume,  "loud",  "medium"  and  "weak".  Ten  trials  were 
made  on  each  fork  with  each  of  these  three  degrees  of  loudness  of 
voice,  the  order  being  as  follows :  one  trial  on  each  fork  from  lowest 
to  highest  and  after  a  pause  from  highest  to  lowest  with  "medium" 
intensity;  from  highest  to  lowest  and  back  to  highest  with  "loud" 
intensity ;  from  lowest  to  highest  and  back  to  lowest  on  "weak" ; 
highest  to  lowest  and  back  on  "medium"  and  so  forth  until  the 
150  trials  were  made. 

These  records  are  summarized  in  Table  IV  and  represented  in 
part  in  Fig.  3.  In  this  table  L,  M  and  W  represent  respectively 
loud,  medium,  and  weak,  other  notation  is  the  same  as  in  the  fore- 
going tables. 

Here  we  find  again,  as  in  the  foregoing  series,  the  tendency  for 
accuracy  in  singing  to  remain  a  constant  in  terms  of  vibrations,  ex- 
cept for  the  extreme  notes,  at  which  there  is  a  decrease  in  efficiency, 
especially  at  the  high  note.    The  form  of  the  average  error  curve  (E) 

'The  force  of  the  blow  changes  the  pitch  of  a  fork,  (See  Winkelmann's 
Akustik,  Vol.  2,  p.  358)  lowering  it  slightly,  but  this  change  in  these  forks 
could  hardly  be  detected  and  certainly  fails  to  account  for  the  error  in 
reproduction.     See  also  Seashore  (21). 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  33 

here  is  entirely  analogous  to  the  form  of  the  curve  of  pitch  discrimi- 
nation referred  to  above  (16,  13,  15  and  26)  but  it  represents  a 
shorter  range,  as  the  voice  has  a  shorter  range  than  the  ear. 

The  constant  error  for  men  here,  as  in  the  foregoing  series,  is  in 
the  direction  of  sharping.  It  is  a  relatively  constant  fraction  of  a 
vibration  for  all  pitches  except  the  highest.  The  records  for  the 
medium  and  the  weak  tones  practically  coincide,''  and  compare  very 
favorably  with  those  of  Series  I.,  but  there  is  a  uniform  tendency 
to  sing  the  loud  reproduction  highest.  The  average  difference  be- 
tween the  loud  and  the  weak  (see  the  G.  C.  E.'s)  is  here  .6  v.d. 
.  This  is  not  a  contradiction,  but  the  reciprocal  of  the  results  found 
in  Series  II:  namely,  that  the  loud  (or  strong)  standard  is  re- 
produced low. 

It  will  be  remembered  that  in  Series  II  the  standard  was  made 
strong,  the  observer  tried  to  produce  a  tone  that  subjectively  seemed 
the  same  in  pitch,  and  that  practically  all  of  his  reproductions  were 
flat.  This  result  in  the  light  of  Series  I,  where  sharping  was  the 
rule,  seemed  to  warrant  the  conclusion  that  the  strong  tone  is 
judged  low.  Now  in  Series  III  we  have  a  confirmation  of  this ;  here 
the  standard  is  of  medium  intensity  while  the  reproductions  are 
varied :  loud,  medium  and  weak.  It  seems  therefore  that  the  in- 
stant the  observer  commences  his  loud  reproduction  he  is  subject  to 
the  same  error  in  judgment  as  was  revealed  in  Series  II,  and  that 
to  make  his  reproduction  subjectively  equal  in  pitch  to  the  standard, 
he  thinks  it  necessary  to  raise.  This  brings  about  abnormal  sharping: 
the  average  G.  C.  E.  of  Series  III  is  -{-1.3  v.d.  as  against  -\-.y  v.d. 
for  Series  I,  where  intensity  differences  were  at  a  minimum. 

The  agreement  of  the  errors  (G.  C.  E.'s)  in  these  two  series 
(II  and  III)  at  once  offers  an  explanation  for  them:  the  error  is 
primarily  one  of  hearing  which  is  basal  and  the  chief  cause  for  the 
error  in  singing.^^  This  is  in  harmony  with  the  contention  of  Kliinder 

'  Medium  and  weak  tended  to  be  confused  by  the  observers  who  would 
frequently  have  to  be  reminded  that  they  were  not  making  sufficient  differ- 
ence between  them.  This  would  imply  that  they  each  seemed  more  natural 
and  less  distinct  than  the  loud,  which  is  borne  out  by  the  fact  that  the 
average  G.  C.E.  for  weak  (Series  III)  is  identical  with  that  for  Series  I, 
i.e.  -i-.7  v.d.  However  it  should  be  noted  that  the  curves  for  weak  are  less 
regular  than   in  Series   I. 

^^  It  is  interesting  to  note  that  in  Series  II  the  high  strong  is  flatted  most, 
while  in  Series  III  the  high  loud  is  sharped  most. 


*>.                     "00-<S-  Tj-rofO  roqf^  '^.  "?^  °9'^.  "^  Q'^Q  9^^  ".  '*'^'^'> 

!>                -^"i-;  NMOJ  H^Mi-;  i/jMirj  oii-^ci  r^oioi  rocs"  coi-Ioii-H 

+  +  +  +  +  I  +  + 

QOi^                     cvii-ioi  MMM  wi-h'  tOMiT)  r'^HHf-^  -tC^'-^  fOi-<fO  rOi-Hro>-< 

g                                     +  I  I  +  +  I  +  + 

..^••.,-cs'-ioq  Ti-o)N  ooio  \oq\tr)  \o"/io  mu^co  "?"?"?  ".  J^oq  Ov 

^|ii>li|^^'  |_;^^^  Mi_;'  r<."t<.  ir)Mio  oin'i-'  Cn<^0\  TJ-i-;ro<N 

EU         +  I  I  4-  +  j  +  + 

!>                w    ■  M  M  M  w  oj    '  oi  •    •     •  ^i  ^^  f^'  r^  oi    '  (N  c^'  M  _;  ^h'  M    ■ 

+  +  I  I  +  I  +  + 
•d 

>M                      f^fO"?  00"^  lOOfO  TtOiO  VOxf-tO  <NcqoO  corj-tv.  Qif^JfOOv 

^  '^                       Ml-;'  mm'  M    i-I   rj  _;■►«■  ro     '   r^  oi   d      '  M    w      ■  M    w    i-i'      ■ 

^                     1  +  +  I  +  4-  +  + 

5"              .-.cjNi-it^  NOPi  NNiN.  O\oq  '^  oosO  \qtN.T}-  i-;f9'-:  '-'.  ^  <^0Q 

a             hJW^W'^'^''^  oii-Ioi  CS^w  '--t  f^'p^  mm'  roc^ro  (Nwoi' 

s                   Su            I  I  I  +  +  +  +  + 

s          I^                w'l-I  c«o'rr)  >-i'i-I  oi'ts  '"'  ■^<~6cs  Mi-ii-i  rji-Hj-I' 

«          ^                        +  +  +  I  +  I  I  + 

§      ^                   OvOics.  q<7q  q  o\oq  ^\q  -^  ^^^  '^.  Q  ^  '^  ^  ^  '^'^'^'l 

'^       "^S                 •    '    •  f^^^ro  csi-h'm  oi'cj  ••■  tvic4i-<  01  f^"'  mmm" 

^     ^                              I  +  +  I  I  I  +  + 

O              ,     ...  00  00  ^  lO  CO  ^  rovo  O  ^i.-.^  li^iom  0\rOt-'  i-HTfin  covo  r^  a\ 

•— 'riJ>W'''  ^^l-JN  oit-Ioi  cok^co  h^^H'*  cioiN  r6c^i-<  cii-H*h4* 

s               su         I  +  +  +  I  I  +  f 

►^              J>                      '?"?'^  rxvovo  vO"^<^  ■-;0\D  r^OOI-%  \OMDO  f>q   f^" "  °*?   '^  "^  "^ 

1^                   ...  „•,_;•  t^j  ,^  5vj  M  i-i     '  M     '  M  M  M  c^'  oi  IN  (vi  w  w  M  i-H 

^•.                              +I+  +  +  +  +  + 
> 

ty        §             ^MOi  '*'^'-:  "?^"?  ^°Q  "?  "^"^  "I"  •>  "?°Q  ^.^  '^  •>  ^i  ^.  "? 

^               -                                                                          I  +  +  I  +  I  +  + 

i-'M'tWcoiotN.  o\o-Ln  qiwoq  <^^.  "-;  <^'-:'7  '^^'^  '>"?'>  ^.  ^]<^'> 

S  U  f^    '  ci  oi  i-H  w  (vj  M  oi  i-h'  i-I    ■  !_;  hH  i-<  oi  w  N  N  !-<'  t^'  N  i-H  iM    ■ 

I  I  +  +  +  +  +  + 

I  I  +  I  I  +  +  + 

'•g                qcoq\  ooqio  lo^Hup  co-^n  '^i^N  c\«.  q\  ^"poi  "?"^'> 

2^                     I  +  I  +  +  +  + 

'— 'W-*.  Wqvqi-;  qi>q  q\qq\  rooqiN  -t-iort  qoqq\  f^vqoj  'f9"1"'7 

S  U  "^    '  <^  oi    '  ^i  r^  i-i  <r>  oi    '  ci  .-;    "  m  d>  i-i  oo  <n  ^-"  oi  r<S  «  fo  w 

I  I  +  I  +  +  +  + 

6      .  •  .  .  .  .  

Oh"  1^  >■  >•  '^  >  Suq 
«                                                                                                       <  >•  >u 

<  << 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING 


35 


'M/lffj 


.._     ^ mv.  ivij 

.  —^•'^  i-nUlM-/ 


103  /J7  176  Zl-/  30G 

Fig.  3.    Volume  of  the  voice  and  accuracy  (Table  IV). 

(12)  that  the  ear  is  the  chief  criterion  for  regulating  the  voice.  But 
the  result  quoted  from  Hancock  (8)  :  that  the  hearing  error  is 
greater  tan  the  singing  error  (when  dealing  with  a  low,  strong 
tone),  together  with  the  fact  (Series  III)  that  there  is  relatively 
more  flatting  with  a  strong  standard  than  there  is  sharping  with  a 
loud  reproduction,  would  conform  to  the  conclusion  reached  by  Stern 
(24)  that  the  kinaesthetic  sense  of  the  singer  is  also  an  important 
factor. 

One  would  expect  a  larger  mean  variation  (m.v.)  for  the  tone 
that  has  the  largest  error,  but  the  table  shows  the  mean  variation 
to  be  practically  equal  for  all  three  intensities  of  sound.  This  may 
be  taken  as  a  mark  of  the  relative  constancy  of  the  motive  for  the 
intensity  error. 

The  agreement  and  the  remarkable  uniformity  in  these  two  laws 
as  shown  in  Series  II  and  III  would  indicate  that  we  are  here 
dealing  with  an  important  factor  of  which  we  must  take  cognizance, 
both  in  the  hearing  and  the  producing  of  musical  tones. 


EXPERIMENTS  SERIES  IV:    TIMBRE  OF  STANDARD 

TONES 

Kliinder  (11  and  12),  Cameron  (4)  and  Sokolowsky  (22)  in 
their  researches  used  organ  tones  for  standards,  while  Berlage  (2) 
made  use  of  tones  from  the  voice.  Having  ourselves  used  tuning 
forks  it  seemed  advisable  to  ascertain  if  timbre  differences  in  the 
standards  affect  the  accuracy  of  reproduction. 


36  WALTER  R.  MILES 

The  standards  selected  for  the  test  were :  a  large  disc  tuning  fork 
(144  v.d.)  sounded  before  a  resonator,  the  dichord  (137.5  v.d.) 
energized  by  bowing,  and  an  organ  pipe  blown  by  mouth.  In  using 
the  latter,  because  of  the  variability  of  the  blow  and  hence  the 
uncertainty  of  the  pitch  sounded,  the  vibration  frequency  of  each 
standard  tone  was  read  on  the  tonoscope  and  entered  in  a  parallel 
column  with  the  reproductions.  The  tones  were  so  far  as  possible  of 
uniform  intensity,  they  were  sounded  for  approximately  2  seconds 
and  after  the  interval  of  i  second  reproduced  on  a,  as  in  "law"  with 
medium  volume  of  voice.  Twenty  trials  were  made  on  each 
standard,  and  because  the  effect  of  timbre  was  the  point  of  interest, 
the  reproductions  were  in  groups  of  five  successive  trials,  the 
standard  of  course  being  sounded  before  each  attempt. 

TABLE  V.     Timbre  of  standard  tones  and  accuracy 


0. 

Fork 
E. 

144 

m.v 

v.d. 
C.E. 

St 
E. 

ring 
m 

137 
.v. 

•5  v.d. 
C.E. 

Pipe 
E. 

Av.  150 
m.v. 

v.d. 
C.E. 

p. 

s. 

Ma. 
V.Z. 

Mi. 

2.5 

I.O 

1.2 

1-3 
2.0 

.6 

.9 

1-3 

•5 
.6 

+2.5 
-  .8 
+  1.2 
+1.2 
+2.0 

1.8 
1.9 
1.2 
2.1 
.6 

•5 
.8 

•5 
•4 
•5 

—1.9 
—1.9 

+1.2 
—1.9 
+  -3 

•9 
I.I 

1-3 
.6 

•5 

•4 

•5 
.8 

•5 
•4 

—  .1 

—  -3 
+  .6 

—  5 

—  .2 

Av.  E. 
Av.  m.v. 
Av.  C.E. 

G.C.E. 

1.6 

.8 

1-5 

+1.2 

1.5 

.5 

1-4 
—  .8 

.9 

•5 

•3 
—  .1 

The  results  of  this  series  of  experiments  are  summarized  in 
Table  V.  Judging  by  the  magnitude  of  the  average  error  and  the 
constant  error,  the  record  is  in  favor  of  the  organ  pipe.  This  is 
probably  due  to  the  fact  that  this  tone  is  most  nearly  like  that  of 
the  human  voice  in  tone-color,  or  timbre.  The  introspections  of  our 
observers,  all  of  whom  have  good  musical  ability  and  were  practiced 
in  observation,  are  however  not  in  accord  with  this.  Four  of  the 
five  stated  that  the  string  was  the  easiest  standard  to  imitate.  P, 
the  one  professional  musician  in  the  group,  felt  that  he  did  best  on 
the  fork.  But  reference  to  the  table  shows  that  it  was  here  that  he 
made  his  largest  errors  and  even  the  largest  made  by  any  observer  on 
that  standard.  S.  stated  that  the  string  was  by  far  the  best  as  a 
standard  but  made  his  smallest  errors,  and  the  smallest  made  by 
anyone,  on  the  fork.  It  must  be  noted  also  that  S.  has  had  more 
practice  with  forks  -than  any  other  member  of  the  group.     Practice 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  37 

is  undoubtedly  a  factor  and  the  value  of  it  for  a  particular  observer 
depends  chiefly  on  what  associations  are  awakened  by  a  given  tone- 
color.  Purity,  for  example,  may  be  thought  of  as  thinness,  and 
secondarily  as  highness  of  tone.  While  tuning  forks,  being  relatively 
pure  and  free  from  over  tones,  are  at  a  disadvantage  on  the  side  of 
richness,  it  is  also  true  that  in  most  groups  the  observers  are  about 
equally  unpracticed  in  singing  with  forks,  which  is  an  advantage 
from  the  standpoint  of  measurement.  The  forks  also  are  decidedly 
more  constant  in  pitch  than  any  other  type  of  standard  tone.  Two 
of  the  observers  noticed  a  tendency  to  imitate  the  timbre  of  the 
standards. 

From  the  above  observations  it  seems  fair  to  conclude  that  rich- 
ness of  tone  favors  accuracy  in  the  reproduction  of  any  particular 
standard." 


EXPERIMENTS  SERIES  V :    VOWEL  QUALITY  AND 

ACCURACY 

Berlage  (2)  introduced  the  problem  of  the  influence  of  vowel 
quality  (or  change  in  the  timbre  of  the  singing  voice)  upon  accuracy 
in  imitating  pitch,  and  made  measurements  on  this  point  for  the 
purpose  of  determining  the  effect  of  mouth  resonance  upon  the 
pitch  of  the  reproductions.  In  considering  the  problem  there 
is  no  thought  of  discrediting  the  results  found  by  Berlage.  The 
tonoscope  method  of  recording  has  enabled  us  to  take  many  more 
records  than  were  used  by  him  in  computing  his  results  and  the 
matter  is  of  such  far  reaching  importance  that  it  seemed  worth  while 
to  include  in  our  study  a  series  on  this  factor,  limiting  our  measure- 
ments to  the  following  vowels : 

u  as  00  in  "toot" 
o  as  o  in  "no" 
a  as  in  "ah" 
^  as  e  in  "there" 
i  as  i  in  "machine" 

In  addition  to  these,  humming  the  tone  was  introduced  in  the  test 
as  the  "hum"  seemed  to  have  no  marked  vowel  quality. 

"  Starch  (23  p.  52)  in  his  conclusions  on  the  effect  of  timbre  in  the  locali- 
zation of  sound  makes  this  statement :  "The  richer  and  more  complex  a 
sound  the  more  accurately  it  can  be  localized." 


^                                 C^     ■   (vj  mm'  ri    h-I   oi  CO  M   ro  •      •      •  ^  ^   ^  cj    i-i   01   ci 

+  +  +  +  I  +  -h 

—                         q  ^  q  ■^  q  t>  ro  ^  q  q  ms  q  m3  ro  -+  oq  cq  oq  oj  oj  q  q 

■^■^  mhh'  f6i-<rr)  ^M-rj-  WMM  '^i-i-rj-  r<-3i-ir0<0 

+  +  +  +  +  +  + 

"O            M     '  _;  M  M     '  01  i-<  r4  oj  w  oi  '     '  ro  i-'  ro  oi  m"  >-<  w 

>                    +  I  +  +  1  +  + 
o 

rt              ^             OOO  ■*<N>-;  ioq\-i-  irsMM  1-;  CfvM:>  "?"."?  "^  ^   "  '^ 

01  i-l  oi  M  M  I-.'  01     '  cN  01  M  o5  hh'     ■     ■  Tt  0)  Tj-  01  w  01  !-<■ 

+  I  +  +  I  +  + 

l-iMI-;  l-I,.;'  f^M(\j  r^n'oi  WI-h'  Oll-Hoi  OlMl-HW 

+  I  +  +  +  +  + 

3              .           vqoivo  -^MrN.  loNc^  '^".P  ""PI"  oi>-;\0  -rj-rt-CNr^. 

•  >             oii-Hoi  Mh-!'  oii-ioA  oqi->'oi  oii-i"  rooioi  oiwi-HH-i 

?             W  gu               +  I  +  +  +  + 

"3       - 

%.     j;                            ^  ■^  "1"  P  °Q  "^  '>'>".  P  °Q  "^  Q  R*  '^  ".  "  ■*  P^''9  "?  *? 

J  "    T  "   +  ""+  ""+  ""+  "     + 

5>                na          M    ■  _;  •    •    •  J,    ■    •  •    .    .  „•    ■  „•  „•  ►J    •  H^    ■    •    • 

-         >■          i  i  I  +  +  I  I 

H^     n!           'S           "^^Q  t  P  *>  '>  ".  P^^  ^  ''P  "1"  "^  P"  "^i  ^!  '^  "^  ".  °°  <-o  oq 

O                                                                                HHt— (I— I  ^H  l-<)-((-HI— l(-H 

I  I  I  I  I  I  I 

•  ••» 

"3      o                      "^  Q  "^  '^  Q^°9  ^  '>oQ  **^.  'n'  9  "^  Q  "?  ^  '^'-^  ■■;  Q  '^  <^ 

S                                                                                 |-IHH)-H  *  I— ll-HHHl-l'l-HI-l  i-HH-l 

^                                                    i  I  I  I  [  I  I 

B        3         [xi    >  bj          '>°^   "?  P^  *>  P'  *">  •>  "^.  O^   't  "^  ^  ".   ".  ^!    '^!   •>  P  °9  ^   "^ 

O                                  "           •          .                     •          •          •  ...  ...  ...  ^      „■      „■  ^      ^          '  M          ' 

^                Su              I  I  I  I  +  I  I 

■— i'     :                            "?'^  ^7  p^t^  •>  '7^.  ".  "T  "i"  ^!  ^.  °o  '^  °0.  P^  *>  "?  P*  P*  P^ 

^•C                             ...  ...  ^'m'  .-■  ^    '  ^  ^^  f^     '  ^^     '     '     ' 

^     '                                       I  +  +  +  +  I  + 

D3     .«                         \q  tN.  '^  p\0  -^  ^.  "?  ^.  "?  "^ "?  '>  f>  '>  '>^.  ^.  P^o°.  ^.  ^ 

s                  +  +  +  +  +  +  + 

V           ^           oqinp  "oqcq  cqcq<rj  "+'7<7  "^P*"  '>'>"7  '^.  °Ovqvp 

^  KH  01                 01  ^      >^  I"" 

i  +  +  +  +  +  + 

rt           *^           '^'^'^.  oqin>o  q\t-^io  inLooi  Onooon  <^oi^  qi^^Dsq 

1  +  +  +  "      +  ""+  "           + 

O                                  vq  vq    I-;  oq  CO    1-;  p\  '^^p  pf>"1'  0<Nm  'Oiopi  t-H    OvMD    i- 

^^                  I  I  +  +  +  I  + 

O              PlJ  iy;i  (J  N  -^  ■^'  W  >.KtJ 

>  >  ^  ^  SuU 

<  >  >^ 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  39 

Three  forks  of  the  large  disc  variety  were  used  as  standards,  the 
pitches  being:  144,  182  and  240  v.d.  and  each  of  these  three  tones 
was  reproduced  to  the  five  vowels  and  the  "hum"  twenty  times,  a 
total  of  360  trials  for  the  individual  observer.  The  test  was  divided 
between  two  equal  periods.  The  order  of  reproducing  was  two  trials 
on  each  fork  to  each  vowel  in  the  double  fatigue  order,  illustrated  as 
follows:  144  to  u,  182  to  n,  240  to  u,  pause,  240  to  u,  182  to  u, 
and  144  to  u;  then  240  to  o,  182  to  0,  etc.,  followed  by  144  to  a,  182 
to  a,  and  so  on  throughout  the  test,  the  order  of  the  vowels  being 
u,  o,  a,  e,  i,  and  "hum."  All  standards  were  presented  to  the  ear  for 
a  duration  of  approximately  2  seconds  and  an  interval  of  i  second 
was  allowed  before  the  singing. 

That  the  vowel  quality  is  a  factor  influencing  the  accuracy  of 
reproduction  is  borne  out  by  the  results  of  the  series  as  shown  in 
Table  VI.  The  average  error  (E)  and  the  mean  variation  (m.v.) 
are  given  merely  for  an  index  to  the  reliability  of  the  record.  They 
are  both  large  as  compared  with  the  constant  error  (C.E.)  which 
is  the  factor  in  terms  of  which  we  desire  to  measure  the  effect  of 
vowel  quality  on  reproduction. 

Although  there  are  characteristic  differences  for  the  three  pitch 
levels  and  for  the  different  individual  observers,  the  results  in 
Table  VI  may  be  fairly  represented  by  a  single  curve  (Fig.  4).    This 


u  'V  a  '  'c  '      c         '        'H 

Fig.  4.     Vowel  quality  of  the  voice  and  accuracy    (Table  VI). 

shows  graphically  the  algebraic  average  of  the  records  (G.  C.  E.) 
for  each  of  the  vowels  and  for  the  three  levels,  144  v.d.,  182  v.d. 
and  240  v.d.  There  is  a  tendency  for  the  vowels  to  fall  into  three 
groups:  namely,  (i)  0  sung  the  lowest,  (2)  a,  e  and  possibly  u 
sung  moderately  sharp  and  (3)  i  sung  decidedly  sharp.  These  facts 
would  seem  to  point  to  the  general  conclusion  that  the  higher  the 
dominating  overtone  in  a  vowel  clang,  the  higher  that  vowel  will 
be  sung.    In  Fig.  4,  u  offers  the  single  exception  to  that  rule. 


40  WALTER  R.  MILES 

The  hum  was  supposed  to  be  neutral  as  it  was  moderately  weak 
and  the  record  was  made  from  the  nasal  breath.  This  assumption  is 
confirmed  by  the  record  which  gives  the  hum  a  middle  place  with 
a  and  e. 

It  must  be  remembered  that  there  is,  in  the  foregoing  records 
which  were  sung  on  a,  a  tendency  to  sharp  by  about  the  amount  of 
sharp  for  a  here.  That  tendency  is  probably  due  to  some  other  cause 
than  timbre.  It  may  therefore  be  suggested  that  a  and  e,  the  vowels 
usually  sung  when  one  is  free,  are  fairly  neutral;  o  (and  possibly 
u)  are  sung  relatively  flat  and  i  relatively  sharp.  This  view,  it 
will  be  observed,  is  confirmed  by  the  hum. 

Our  results  seem  to  differ  radically  from  those  of  Berlage  (4), 
second  part  of  item  4,  in  the  observations  which  are  common  to 
both.  But  our  method  also  was  radically  different ;  moreover,  his 
conclusion  (item  4)  is  somewhat  modified  when  we  read  in  his 
article  p.  76  where  the  results  of  the  vowel  experiments  are  dis- 
cussed. "Accordingly  one  may  look  upon  a  slight  increase  in  the 
variable  error  as  probable  with  vowel  change"  (i.e.  when  the  ob- 
server tries  to  reproduce  his  own  pitch  but  on  a  different  vowel)  .  .  . 
"other  generalities  cannot  be  deduced  for  the  table  ..." 

These  results  in  reference  to  vowel  quality  are  of  so  far  reaching 
significance  for  speech  and  song  that  we  may  not  venture  further 
discussion  for  the  matter  must  be  made  a  special  object  of  investiga- 
tion for  verification  of  the  empirical  data  and  in  search  of  an  inter- 
pretation. It  seems  safe  however  to  proceed  in  our  work  using  "a" 
as  the  vowel  quality  for  reproductions. 

EXPERIMENTS  SERIES  VI :    ACCURACY  IN  SINGING 

Having  gained  some  insight  concerning  the  influence  of  voice 
range,  standard  tone  intensity,  *voice  volume,  standard  tone  timbre, 
and  voice  timbre,  on  the  accuracy  of  voice  control,  we  now  turn  to 
the  main  problems  of  our  research.  These  may  be  restated  as 
follows :  ( I )  What  is  the  average  error  of  the  human  voice  in 
reproducing  the  pitch  of  a  tone?  (2)  What  is  the  average  minimal 
producible  change  of  the  voice?  (3)  Is  there  any  general  tendency 
to  sing  sharp  or  flat?  (4)  How  does  the  average  performance 
of  men  and  women  compare  on  the  above  three  points?  All  the 
studies  referred  to  in  the  historical  account  contain  results  which 
cast  light  on  some  of  these  problems.    But  in  almost  every  case  these 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  41 

results  and  problems  are  secondary  to  the  main  interest  of  the  study; 
and  moreover  the  number  of  observers  and  observations  is  usually 
quite  limited.    In  Series  VI  therefore,  we  have  made  these  problems 
the  central  issue  on  a  large  group  of  persons  to  give  our  results 
significance  as  norms. 

Apparatus  and  method 

Standards.  With  the  aid  of  the  tonoscope,  eleven  large  disc  forks 
were  tuned  to  the  following  pitches:  128,  128.5,  129,  130,  131,  133, 
136,  140,  145,  151,  and  158  v.d.  The  series  of  pitch  increments  be- 
tween the  forks  was  therefore:  .5,  i,  2,  3,  5,  8,  12,  17,  23,  and 
30  v.d.  as  measured  from  128  v.d.  This  series  of  tones  was  used  for 
men.  For  the  women  a  second  set  was  provided  on  256  v.d.  as  a 
basis,  namely,  256,  256.5,  257,  258,  259,  261,  264,  268,  273,  279, 
and  286  v.d.  In  this  second  set  it  will  be  noted  that  the  same  pitch 
increment  (absolute)  were  used  as  in  the  128  v.d.  set  instead  of  the 
relatively  equal  increments.  In  this  respect  the  procedure  was  based 
upon  the  conclusions  reached  in  Series  I. 

Koenig  resonators  were  provided  for  each  set  of  forks.  As  the 
increments  were  small  it  was  found  that  one  resonator  would  speak 
sufficiently  well  to  several  tones.  In  the  case  of  the  128  set  three 
resonators  were  used:  first,  128  v.d.  to  and  including  136;  second, 
140  and  145  v.d.;  and  third,  151  and  158  v.d.  For  the  higher  set 
two  resonators  were  found  sufficient :  first,  256  v.d.  to  and  including 
268  v.d. ;  and  second,  273,  279,  and  286  v.d.  Both  series  of  forks  as 
reinforced  by  the  resonators  gave  tones  of  pleasing  quality  and 
medium  intensity. 

Observers.  Two  hundred  and  one  individuals,  ninety-four  men 
and  one  hundred  and  seven  women,  took  the  test  which  is  about  to 
be  described.  This  number  comprised  those  enrolled  in  the  elemen- 
tary psychology  courses  in  the  University  of  Iowa,  1912-1913.  Of 
these  about  one  hundred  fifteen  were  sophomores ;  the  remaining 
were  upperclassmen.  None  of  them  had  had  any  practice  in  this 
test.  Among  them  were  some  excellent  vocalists  and  some  others 
who  claimed  never  even  to  hum  or  whistle  and  to  have  difficulty  in 
recognizing  old  and  familiar  tunes  if  unaccompanied  by  words.  No 
one  was  excused  because  of  his  inability  and  no  one  was  selected 
because  of  ability,  for  it  was  desired  in  so  far  as  possible  to  secure 
what  might  be  considered  an  average  group.     A  previous  lecture  on 


42  WALTER  R.  MILES 

the  measurement  of  musical  capacity  had  successfully  aroused  the 
interest  of  the  observers  so  that  they  entered  into  the  experiment 
with  zest,  many  of  them  desiring  to  secure  their  individual  results. 

The  charge.  The  instructions  were  given  by  word  of  mouth  to 
each  person,  although  the  appointments  were  so  arranged  that  one 
observer  was  present  while  another  was  taking  the  test  and  so  be- 
came familiar  with  the  procedure  before  he  actually  entered  upon  it. 
Supposing  the  observer  to  be  a  man  the  instructions  would  be  as 
follows : 

"Mr. ,  we  have  here  a  series  of  eleven  tuning  forks.    This 

one  (striking  the  128  v.d.  and  presenting  it  before  the  resonator) 
is  c  below  "middle  c",  it  is  a  tone  of  128  v.d.,  the  lowest  tone  in  the 
series ;  we  will  call  it  "o".  This  one  (striking  and  presenting  the  in- 
crement fork  30,  158  v.d.)  is  considerably  higher  than  o  as  you 
easily  notice,  and  is  the  highest  one  in  the  group.  These  other  forks 
all  represent  pitches  between  the  two  which  we  have  sounded.  The 
test  to-day  consists  in  singing  these  eleven  tones  one  after  the  other 
as  they  are  given.  They  will  be  presented  in  pairs.  First  we  will 
sound  the  o,  the  lowest  one  of  the  tones;  you  will  listen  carefully 
to  it  and  then  sing  a  tone  of  the  same  pitch.  Immediately  after  your 
singing,  the  highest  tone  in  the  group  (30,  158  v.d.)  will  be  sounded; 
you  will  listen  and  sing  that  one.  Then  the  o  will  be  sounded  again 
and,  after  you  sing  it,  there  will  come  the  next  to  the  highest  tone 
(23,  151  v.d.)  ;  and  so  on  we  will  come  down  one  step  at  a  time 
always  reproducing  the  o  before  each  of  the  interval  forks.  When 
you  have  tried  all  the  tones  in  the  series  you  will  go  back  over  them 
in  the  reverse  order.  Simply  imitate  as  nearly  as  possible  the  pitch 
of  each  tone  as  it  is  given,  always  remembering  that  the  o  is  the 
lowest  one  in  the  series.  Sing  all  the  tones  with  a  natural  voice 
volume  and  use  the  vowel  "a"  (a  as  in  "ah")  and  whenever  you 
feel  dissatisfied  with  any  trial  ask  for  a  repetition." 

Following  these  instructions,  in  order  to  put  the  observer  at  ease 
and  to  satisfy  his  curiosity,  the  experimenter  gave  a  brief  explanation 
and  demonstration  of  reading  on  the  tonoscope. 

The  test.  The  forks  were  presented  to  the  resonator  by  a  helper 
who  gave  his  attention  solely  to  the  task  of  sounding  the  tones  in  the 
right  order  and  with  as  nearly  uniform  intensity  and  duration  as 
possible.  The  tones  w^ere  sounded  with  medium  intensity  varying 
towards  the  "weak."    The  observer  sat  on  a  high  stool  or  stood  at 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  43 

the  side  of  the  instrument  in  a  position  which  kept  him  from  seeing 
his  own  record.  He  sang  the  tones  into  a  metal  speaking-tube 
placing  the  lips  lightly  against  the  fingers  of  the  hand  which  grasped 
the  mouthpiece.  The  arm  was  supported  by  an  adjustable  rest  and, 
so  far  as  could  be,  strain  and  unnaturalness  were  avoided. 

A  few  preliminary  trials  were  given  on  increment  0-30  in  order 
that  the  observer  might  find  himself  becoming  somewhat  familiar, 
not  only  with  the  tonal  range  covered  by  the  standards  but  with  the 
experience  of  taking  pitch  from  a  tuning  fork.  The  series  was  then 
given  in  pairs  in  the  following  order:  0-30,  0-23,  0-17,  0-12,  0-8. 
0-5,  0-2,  o-i,  0-.5;  0-.5,  o-i,  0-2,  etc.,  back  to  0-30.  The  complete 
test  consisted  in  singing  the  series  thus  five  times.  This  gave  one 
hundred  reproductions  of  the  0,  and  ten  on  each  of  the  increment 
tones,  a  total  of  two  hundred  tones  for  each  observer.  This  series 
therefore  contains  forty  thousand  records.  The  test  as  outlined 
could  not  be  performed  with  care  in  less  than  30  minutes.  In 
some  cases  and  especially  with  non-musical  persons  a  much  longer 
time  was  required  than  this. 

Throughout  the  test  we  endeavored  to  keep  the  observer  seriously 
trying  to  sing  the  exact  pitch  of  the  forks.  To  this  end  it  was  deemed 
desirable  to  ofi^er  some  encouragement,  especially  during  the  first 
fifth  of  the  experiment,  no  matter  how  poor  or  good  the  record. 
It  was  observed  that  encouragement  did  not  cause  the  singers  to 
be  self-satisfied  or  careless  but  rather  served  to  make  them  try  the 
harder.  It  helped  moreover  to  create  an  atmosphere  of  ease  and 
naturalness.  But  while  there  was  encouragement  there  was  also 
some  criticism.  If,  for  example,  the  observer  was  singing  the  o 
flat  5  or  6  v.d.  regularly  he  was  told  to  listen  more  carefully  to  the 
standard  and  to  make  sure  that  he  had  the  right  pitch  but  no  intima- 
tion was  given  as  to  the  character  of  the  error.  Little  rest  periods 
of  twenty  seconds  were  rather  frequent  and  were  found  to  be  of 
much  service.  Many  times  it  was  noted  that  after  such  a  period  the 
errors  were  decidedly  smaller  than  before. 

A  few  questions  concerning  the  observer's  musical  education, 
voice  range,  and  ability  to  play  and  sing  were  asked  during  or  fol- 
lowing the  experiment  and  the  answers  together  with  some  com- 
ments regarding  his  performance  of  the  test  were  made  matters  of 
record. 


44  WALTER  R.  MILES 

Justification  of  procedure 

Before  considering  the  results  of  this  series  it  remains  to  justify 
the  form  of  procedure  as  outlined  above  in  the  light  of  the  sources 
of  error  revealed  by  our  previous  experiments  and  by  those  of  other 
investigators. 

Voice  level  of  test.  Our  experiments  (Series  I)  on  the  accuracy 
of  pitch  singing  within  the  voice  range  demonstrated  that  the  errors 
are  relatively  smaller  on  the  higher  tones.  Unpracticed  observers 
however,  will  much  more  readily  try  a  tone  that  is  medium  or  low 
than  one  that  is  high.  It  therefore  seemed  best  for  general  testing 
to  choose  a  voice  level  which  all  would  recognize  as  being  well  within 
range.  The  selection  of  128  to  158  v.d.  for  men  and  of  256  to  286 
v.d.  for  women  is  thus  the  result  of  considerable  experience  in  test- 
ing groups  of  individuals,  and  seems  further  justifiable  on  the 
grounds  of  pitch  discrimination  as  previously  stated. 

Forks  for  standards.  Tuning  forks  were  retained  for  standards 
even  though  the  records  of  Series  IV  indicate  that  the  organ  pipe 
and  dichord  can  be  imitated  more  accurately.  Forks  are  very  sim- 
ple, easily  manipulated,  of  practically  constant  timbre,  and  at  the 
same  time  reliable  in  pitch.  And  if,  as  in  our  test,  a  series  of  tones 
differing  from  each  other  by  slight  degrees  of  pitch  is  desired  to  be 
sounded  in  rapid  succession,  tuning  forks  are  the  most  reliable 
apparatus.  Furthermore  they  are  used  so  little  for  general  musical 
purposes  that  in  testing  with  them  no  group  of  observers  is  given 
undue  advantage. 

Many  standards  vs.  one  standard.  Berlage  (2)  found  that  his 
observers  could  reproduce  their  own  voice  tones  more  accurately 
than  tones  given  by  some  one  else,  the  increase  of  precision  show- 
ing itself  chiefly  in  a  decrease  of  the  constant  error.  We  have  fre- 
quently noticed  a  tendency,  which  is  a  corollary  of  Berlage's  con- 
clusion. Observers  when  making  successive  trials  on  the  same 
standard  very  often  reproduce  their  own  reproductions  rather  than 
make  new  efforts  at  imitating  the  real  standard.  The  observer  finds 
it  much  easier  to  reproduce  his  own  previous  tone,  duplicating  the 
muscle  tension  and  mouth  resonance  which  he  experienced  at  that 
time  and  felt  to  be  satisfactory.  Indeed,  even  though  he  conscien- 
tiously work  against  this  tendency,  he  can  not  overcome  it  entirely  if 
engaged  in  making  successive  trials  where  the  pauses  between  are 
brief.    This  is  confirmed  by  the  fact  that  frequently  when  observers 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING         45 

for  some  cause  or  other  have  been  dissatisfied  with  attempts  and  de- 
sired new  trials  giving  them  immediately  they  would  in  the  new  trials 
unconsciously  repeat  the  identical  pitch  given  before.  This  same 
tendency  has  sometimes  been  evident  even  in  large  and  unusual  errors 
which  the  experimenter  might  rule  out,  asking  for  new  trials.  In  view 
of  these  considerations  it  seemed  best  in  our  general  test  to  adopt 
the  principle  of  many  standard  tones  and  no  successive  trials  on  the 
same  tone. 

The  increments  between  the  forks  were  made  small  and  of  vary- 
ing magnitudes  for  two  reasons :  first,  in  using  these  small  increments 
we  do  not  complicate  our  work  with  the  factor  of  musical  intervals, 
and  second,  in  using  a  series  of  small  increments  we  make  possible 
the  measurement  also  of  the  ability  to  make  faint  shadings  (sharp  or 
fiat)  in  the  pitch  of  the  voice.  The  selection  of  increments  is  arbi- 
trary. These  particular  steps  were  chosen  because  they  have  been 
found  satisfactory  in  work  with  pitch  discrimination  (21)  at  the 
level  of  435  v.d.  and,  as  stated  before,  extensive  research  by  Vance 
(26)  and  others  shows  that  pitch  discrimination  is  practically  con- 
stant in  terms  of  vibration  frequency  in  the  middle  range  of  tonal 
hearing  here  covered.  This  is  also  the  ground  for  making  the  in- 
crements for  the  women  the  same  number  of  vibrations  instead  of 
the  relative  parts  of  a  tone,  in  which  case  they  would  have  been 
doubled. 

Sounding  the  two  tones.  Seashore  and  Jenner  (19)  employed  the 
method  of  "least  producible,  or  minimal,  change".  The  observer 
sang  the  standard  or  a  tone  at  a  given  interval  from  it  and  then  re- 
produced his  own  reproduction,  save  that  he  made  it  "the  least  pos- 
sible" sharp  or  flat  according  as  the  experimenter  might  direct. 
While  this  will  undoubtedly  become  a  standard  method  in  extensive 
work  with  an  observer  it  is  not  suited  to  tests  of  a  single  sitting, 
first,  because  ability  is  rapidly  improved  by  practice  and,  second, 
because  the  observer  tends  to  be  easily  satisfied  with  his  effort.  The 
better  way  is  not  to  rely  on  the  changing  subjective  standard  of  the 
observer  but  to  provide  a  series  of  constant  objective  increments 
and  give  him  the  opportunity  to  find  his  own  level  as  by  the  method 
of  constant  stimuli  in  lifted  weights  or  pitch  discrimination.  Such 
a  series  has  been  provided  in  the  standards  and  increments  men- 
tioned above. 

Order  of  standards.    Manifestly  the  standards  might  be  presented' 


46  WALTER  R.  MILES 

to  the  observer  in  any  one  of  a  number  of  different  orders.    After 
trying  out  the  matter  thoroughly  with  the  help  of  three  good  ob- 
servers we  selected  the  order  of  presentation  above  described  for  the 
following  reasons:  (i)  to  give  the  tones  in  pairs  (0-30,  0-23,  etc.) 
takes  direct  advantage  of  all  the  latitude  which  the  series  provides. 
Most  observers  can  easily  detect  the  difference  0-30,  while  many 
(theoretically  about  25  per  cent.)  would  be  baffled  to  find  a  differ- 
ence between  23  and  30;   (2)  to  begin  with  the  largest  increment 
and  work  towards  the  smallest  has  the  double  advantage  of  es- 
tablishing confidence  in  the  attitude  of  the  subject  and  of  stimu- 
lating effort;   (3)  to  give  the  increments  in  a  series  and  in  double 
fatigue  order  rests  the  voice  from  the  unusual  strain  of  making 
the  least  producible  change,  and    (4)    to  explain  definitely  at  the 
beginning  of  the  test  that  all  the  increments  are  in  one  direction, 
i.e.  above  the  o,  simplifies  the  problem  and  puts  it  more  definitely 
under  control  than  if  uncertainty  as  to  change  of  direction  in  stand- 
ards were  allowed.    The  test  is  therefore  not  to  measure  the  judg- 
ment for  direction  of  pitch  difference  but  the  judgment  and  expres- 
sion of  the  amount  of  pitch  difference  between  two  tones.     In  pitch 
discrimination  it  is  well  known  that  much  depends  upon  the  direc- 
tion of  the  expectant  attention.^-   And  should  we  present  the  stand- 
ards of  our  test  in  a  chance  order  we  would  complicate  it  exceedingly 
at  the  critical  point  of  the  smallest  increments. 

Time  intervals.  At  the  very  beginning  of  the  test  the  intention 
was  to  allow  an  interval  of  i  second  between  the  breaking  off  of  the 
standard  tone  and  the  singing  by  the  observer.     But  the  method 

^An  idea  of  the  influence  of  this  same  source  of  error  operating  in  the 
field  of  singing  may  be  gained  from  the  following  illustration.  The  author 
in  instructing  a  very  fine  observer  thoughtlessly  said,  (the  error  was  alto- 
gether unintentional)  ;  "We  have  here  two  forks,  the  first,  128  v.d.,  and  the 
other  one  3  v.d.  higher,  131  v.d.  You  will  please  sing  them  one  after  the 
other.  I  will  give  the  lower  one  first."  Then  the  forks  were  presented  and 
reproduced  as  directed.  When  we  came  to  the  twelfth  trial  the  observer 
remarked :  "I  seem  to  feel  strain  to  bring  the  131  v.d.  up".  In  the  moment  of 
reflection  following  this  remark  the  writer  recognized  that  he  had  made  a 
mistake  in  instructing  the  subject,  as  the  so-called  "131  v.d."  was  really  3  v.d. 
"  lower  than  128  v.d.,  or  125  v.d.  We  find  in  the  twelve  trials  made  that  the 
average  reproduction  of  128  v.d.  is  123.6  v.d.  while  the  average  pitch  given  for 
the  supposed  131  v.d.  (really  125  v.d.)  is  124  v.d.  The  misunderstanding 
and  therefore  expectant  attention  changed  the  direction  of  the  reproductions, 
and  brought  in  much  larger  constant  errors  than  are  usual  for  this  indi- 
vidual.   It  should  also  be  noted  that  the  errors  are  minus. 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  47 

was  soon  given  up  as,  in  this  case,  cumbersome  and  unpractical,  and 
furthermore  we  did  not  care  to  compHcate  our  test  with  the  factor 
of  tone  memory.  (See  Berlage  (2)  and  Sokolowsky  (22)  ). 
The  observers  in  their  usual  singing  with  musical  instruments  make 
no  such  perceptible  time  intervals.  They  sing  with  the  tones  of  the 
instrument,  perhaps  holding  them  somewhat  longer  than  is  done  by 
the  instrum.ent.  When  the  standard  has  been  sounded  the  atten- 
tion is  centered,  the  muscles  of  the  larynx  almost  involuntarily 
assume  a  particular  tension  and  it  is  unnatural  to  wait  for  the 
beating  of  a  metronome  or  some  other  signal  to  begin  singing. 
If  the  unpracticed  observer  is  told  to  make  his  own  interval,  un- 
less checked  up  diligently,  he  will  very  soon  be  making  intervals 
that  are  exceedingly  short,  if  indeed  he  is  not  singing  simultaneously 
with  the  standard  tones.  The  method  followed  therefore  was  to 
sound  the  forks  for  approximately  i  second,  encouraging  the  ob- 
server to  begin  his  tone  during  the  sounding  of  the  fork  and  to  hold 
it  longer  than  the  fork. 

It  may  be  objected  that  one  might  sing  fairly  accurately  judging 
simply  on  the  secondary  criterion  of  beats  between  his  voice  and  the 
standard  tone.  Helmholtz  indeed  (9  p.  326)  suggests  this  as  a 
convenient  method  for  the  singer  to  use  for  checking  his  own  accu- 
racy in  practice  exercises.  While  it  would  be  possible  for  a  highly 
practiced  observer  it  can  hardly  have  much  influence  in  our  test.  The 
author  made  it  a  point  to  question  frequently  regarding  the  way 
observers  judged  of  their  success  in  reproducing  tones  and  was  not 
able  to  find  any  one  who  knowingly  made  use  of  this  criterion.  It  is 
however  quite  possible  that  the  roughness  of  6  or  8  or  more  beats 
per  second  may  occasionally  have  caused  some  observer  to  be  dis- 
satisfied with  his  attempt.  But  the  tonal  fluctuations  and  adjust- 
ments which  are  necessary  to  bring  about  a  lessening  of  the  fre- 
quency of  beats  between  the  voice  and  an  outside  standard  are 
easily  recognized  with  the  tonoscope;  no  such  "finding"  process 
was  observed. 

Another  time  interval  which  must  be  considered  is  that  between 
the  o  (128  or  256  v.d.)  and  the  increment  fork  of  any  particular 
pair.  In  order  that  the  standards  for  minimal  change  of  voice  may 
have  their  greatest  value  the  interval  indicated  must  be  as  short  as 
possible  admitting  of  a  quick,  direct  comparison  of  tones;  other- 
wise the  test  practically  resolves  itself  into  the  singing  of  a  single 


48  WALTER  R.  MILES 

tone.  Hence  the  presentation  of  the  increment  fork  followed 
immediately  upon  the  close  of  the  observer's  reproduction  of  o, 
the  subject  being  encouraged  to  make  the  reproduction  about  i 
second  in  length.  The  increment  forks  were  struck  while  the  o  was 
being  reproduced.  This  was,  however,  no  distraction  as  only  a 
slight  blow  on  the  practically  noiseless  sounder  was  necessary,  and 
the  forks  could  not  be  heard  until  presented  before  the  resonators. 
Following  the  reproduction  of  each  increment  fork  there  was  a 
period  of  about  2.5  seconds  before  the  next  sounding  of  o. 

Other  factors.  In  the  matter  of  intensity  of  standard  and  in- 
tensity and  vowel  quality  of  the  voice  we  took  direct  advantage  of 
our  previous  work  and  adopted  such  conditions  as  would  give  the 
most  normal  results  according  to  those  findings.  By  the  use  of 
resonators  at  a  considerable  distance  from  the  observer's  ear  w'e 
found  a  satisfactory  means  of  controlling  the  intensity  of  the 
standards, ^^  while  the  intensity  of  the  voice  had  to  be  judged  sub- 
jectively and  watched  by  the  experimenter.  And  in  the  selec- 
tion of  "a'  we  are  using  that  vowel  quality  which  according  to 
Berlage  and  our  own  results  afifects  least  the  constant  error  of  the 
reproductions. 

Tables  of  data 

The  constant  error  (C.  E.)  and  mean  variation  (m.v.)  were  found 
for  the  ten  trials  on  each  fork  of  the  ten  pairs  given  in  the  test. 
These  twenty  C.  E.'s  and  twenty  m.v.'s  for  each  individual  tested 
are  embodied  in  Table  VII,  which  has  been  divided  into  two  parts, 
A.  and  B.,  for  the  men  and  women  respectively.  In  the  first  column 
of  the  table,  at  the  left,  are  given  the  numbers  which  stand  for  the 
individual  observers.  This  numbering  is  in  no  sense  a  ranking,  but 
simply  for  convenience  in  handling  the  data  and  aid  in  identifica- 
tion. Odd  numbers  are  used  throughout  to  refer  to  women  and 
even  numbers  to  men.  The  second  column  from  the  left  shows  the 
C.  E.  and  m.v.  (the  latter  is  under  the  former)  for  the  ten  trials 
on  o.  when  used  in  the  pair  0-30.  The  same  measures  for  the  ten 
trials  on  variant  (or  interval)  tone  30  are  given  in  column  three, 
and  each  of  the  successive  smaller  increments  are  represented  in 
the  same  manner.     The  arithmetic  averages  for  the  constant  error 

"  It  is  possible  that  the  pitch  of  a  standard  is  not  only  varied  by  its  intensity 
but  also  by  its  position  when  held  near  the  ear. 


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Tf  f^T 


■'+''+''+"l"i"?'^:"+"+'|"+"+''"  ■■"?'?"  ■ 


5  +-;-;-+  °-?'j-7-T-|-+-+  :?-+"+-+-?  +   i   °  +  +"t  ?.  +  +  +  ?  +  +  +    i    i 

«  ^3J-JS3.;j»j~j-jp-}«j-j-4:-|-^:^|-:|;-5^"j"Y-'^-|-.|--.:f":f-=;'-jj:-5™f-5.":f-f ■■^-+-jf-4;";f-j"!f''5.-'4:-':f'J-|-:^~j  ^  +  +  +  ?  +  +  +  +  +  +  ?  +  +  +  +  +  +  +  j  +  +  +  J  ?  +  |  +"  +  "+  +  +  +"+"+  ?*?'+'?"*  :f  +  *  +  +  +  +  +  +  +  +  +  +  +  ?  +  +  ?.T  +  + 


T    +    +    T    +     I 


.  .,  -,   :■:-.-;;-■■   T  3»;'g  -TJT  joj^e-  ^^=3  :;7'S'S  32  2 


+"?  r 


*  |'j'$=}'i-t-t'?-:f'-+"?"*-?-r  +"+  4:  +  t  *"*  +  '"*"  +"*  +T-  +  *  +  +  +  +  *  +  +  i"r+ +  +  »  +  ?  +  +  ?  +  *  +  *  +  +  +"+"+:  |'|"$'$"j  ?  t  +  +  +  +  •"ijf-y-:;-^-'^:"^-^-'^":?.  :fjt  +  +  +  +  +  ^-+  +  +  t  +  +  ?:f  +  +  jf  + 


?  ?:! 


+  +  + 


+  +  + 


rrr 


I)  «c^ii?fl  -^c  cc  (if.  T«!a5»;  1 


I 


fliip«q  isoNQujq-o. 


i"*" 


q  TOS'JSQq  iTfl  f^  "f 


"+"4'*  4^"  +  "?"  +  "+"  +  "' 


"'-°   ;^"+"^^-+-+''+"+    T    +  ■?■  +"+"■¥"!    +"+"+"    "+"+"+ 


T"?- 1  "+"+'■ 


-r-r-^  ■»«'fla)T«<*  Ro«« 


1-«  TleflB-fl*  TO  T^'0«i23'^*  ""^  "^ 


?SS'S*3S3 


1-1  T>>-7«rTS0.«ia«o«((!»i'iB-'O,*;«TP>oqc««*Qq  T-It1 

+    4-+T+    +    +    +    tT     T+    +   +    f    +    + 


,,.^.,„ 


+"!"+"+   +-^"T"^    f-i-^-f^+'T    +'+"+"+'+    ""+"?"+"?    ?"t"T''-?"+"*"+"?    +   +    t"+"T"^~t"+   +   ?-~+"T"+"+"      +"+   +   +   +  +"+  +   +   +"+"+   +"+"+   +         +   +   ^   + 

■+"j"^~T  +"+"7*'^  f-+"+-f   +  T  +  +"?"+  +"     +"T"     T"T"'r"'T  ?'"r'"+'"+"H^  ^_---_«^-^-,|-^--  +"+"h^  ?*■■?■"+  +"?"■?■  +"+  +  +"+  i  +  +  +"1"'+  +  +  +  +  +  ■+  +  + 


^    4-  WIS-*" 


?  §■  f  ^ 


ll=? 

f 

? 

+ 

<•>? 

S-"-5 

s 

3»-S 

:  o<s 

?^"? 

t 

5e«-? 

+ 

1 

sa  ft"  i;« 

e 
A 
■? 

+ 

3B3-«K 

+ 
-+ 

s. 

l«'°f| 

s 

^^"'B 

- 

5 

^rtij 

1- 

f*-3| 

"     -  -  I 


«    -        ~+ 
"+ 


^'■S>?  ^-s>? 


-   T"? 


:  ? 


+    +    +    +    +    +    |    +    +    +    +    +l+    +    +    +    +    +    +    +T+    +    +    f7+4:+     +    +    +    +    +    +T+    +    +    +    +    +    +     +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +T+    + 

+  ti-f  +  +  +ffTTtT'+?+T  +  ?TTTi+  +  +  T  +  T    '    '    i44+ifTTf7iiT  +  +  +  +T+i    i7++iT'+TTii    iTTT7''++'    I'^i'f+i    |-TitTTT++7+TT+T 
+    1+^       +-fi        Ti7iT+i+TT+rTri+++l    +    iTTl+  +  +  +ri    iTTlTi    +^  ^  +  T*TTi+Tl    I     ill    ii 


V\    T   *  +  ^  + 


"T'^  f  *  ^n 


'^^B*^3*-'"y^°''' '''^'^"' ''" 3'"'2'^2*''  ^T". •?■ 


r^-rri-'r^  v^-vrv 


I  T"T''T"7  T'"?"+  +  T   T  +  T 


+''+"T'?'' 


-r+-t  T-T  T  T-ri" 


,„j..„.. 


«^c.^«^««-,;|     _jn2-,y«_,,« 


-•fl  «lllf«.«!  T 


''S5S!£)J2'*'SI!JS25  2S?5S!22JA5"3^riS'322.S'i^?3S'S;^;:;'3J?2S53J^"'^S2'^f -JRI-^T^a  2q'*>«!'P'fit;VJ-'»«3iy-)'q  q'^«!r"^'>5'J'^T'l')PT«!'?'^33<*'-'iq»-a!  o<i-r>-.!f  "rTS>e'"5t?Toj"!  q-- -^-n" '-qoo  a 'jo?fi.nuj-->n>?-tj'nTPoqo?<!t>r»«!.qi^uj-^-»-T.5q>ni><ji?oqs^tii^'7uii;oq -■>>«- ««>«<>! 

?-rrrrnTP!'rr?'fTF*''rtTrr?-rn7-T^I'rn-r11'rT^fTrT-T-T=^^ 

+  +  +  +  +  +  }  +  +  +  +  +  +  +  +  +  +  +Tf  +  +-:^  +  +  +  +  3.  +  3.  +  +  +  +  ?  +  +  3  +  +  +  +  +  ?-  +  +  ?T  +  +  T  +  4-3-  +T  _"|";:";f"jf  2»a»:p  41  ^»^,jp™^™^  .,|.;j.-^».«»»^,^.--.-;^  +  +  +  ^"«~i  +-^  +  3  +  3  +  3 


qq  Tjj^i^'D 


f'''^*q  P  '^^'S  P  'J'T'O'^'^  ""^P^-t^jq"-*!  f  7  f>  5  =?  5 '2'^  525q=flTa^1P1  "7^  T-t*-  fP  TI  ^t?*  1  '^--qs^"  n  ■n<.«>*9)<J  n--  CT.ir.-i.  .-ininqq(-.oOio-IT'>'>ortici-fmi.  «  ^TT-'Q^'^'-tTn'o-  ";"iq>o-t'»-«'r  ")T»io  "  ^o  o  «  n   o  o  r.  o»o  -  -  -rnni-.OHtMn-ioon  ono  ptio-MS-  cote  i^—soe«  in-  TiO  •)  -  fl«  "i>>0  tfJTOO  h-no  n-fliq 


rrri 


T-J-yqqqi^"? 


frt- 


^...j.f... 


T  +  +T  +  5L  +  +  3  +  +   I   +  +  +  +  +  +  +  +-+  +I+  +  +  3-  +  +   +:t  +  +  "•■+  :^"+  J  +  :f  +  ?  +  +  +  +  +"+"^'+"1  3;"j"j  _».~«™,jj,,n«-,^»«.^„^, -„„ 


r,.?<^»i^Qq.^l^.BqFtB;-n-.vi--»u>-;<>^>|.q-74q>qqK^q'ir} 

"n^i'iT-n-q-q"-*q''«  4w  «q>n-.^^»q-  —  '5.>o^-t'»>^ 

+  i-f  +  +  +  :j  +  +™  T  +  T  +  +  I  +  +  + 

f-r°  I  ^  i  r^  rrVrrl  1-1-""-+ 


?  T"T''T'i%  ^  i"fTT-rT  T  +  +"+  rri  rrrvvrrri  ^  v^"\~i  r 

■>'fl'^31'2SSSS?^  .^t^(,-r.^Bi«?«-Q-5(>^r,^(iq-^q,,<^q.;5q<9~t>Tqq<>«yq-T5-7>>t»»'n'7qqh.'n--r,ino.«n 

ITI+  +  T+I   +   ITI 


■Yi^i^f 


m  1 ' 


■f"t"T    1*7  4"+  ?"7  +-f-t-7^  T" 

T  "-3<>!'P-7' 


"%  T" 


+  'rt  f-t-rf"T"t 


T    I    I   +  +  +  t  4  +  +  +  TV  jp  T-|    T":f  t   t  +  +  ^  +  ^"hL  5:  ^^"5  3  3  +-?-+''+-f  3  +  T  3 


"t~+"T"r 

=?Tqq'P"5i?«iP'^ti<!  3'ii"">'ot-<?'if>5  3*S'5f^'>;*"'''^ 

!"  *  T-fT''T-T"+  T"'^-T"+'+  T 


f •*!•**  ri-fr*- 


+T+++++++++ 


?r^:j-J-'f|3fps'spi|ipi''^5pps'='j'5^spppj-3-jj;::p^'j:p8=j333j:'f;pp|S3:a=!jp^^ 


■^f-i-r^^i^f 


c 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  49 

(C.  E.)  and  the  mean  variations  (m.v.)  on  both  standard  and 
variant  are  presented  in  the  two  columns  headed  O.  V.  (Arith- 
metic). The  algebraic  averages  for  the  constant  errors  (C.  E.)  on 
both  standard  and  variant  are  given  in  the  two  O.  V.  columns  at  the 
extreme  right  of  the  table.^* 

The  consolidated  footings  for  Table  VII,  section  A  and  B,  are 
given  in  Table  VIII.  The  top  notation  is  thus  the  same  as  in 
Table  VII.  A  contains  the  final  footings  for  men  and  B  for  women. 
The  footings  are  set  out  as  follows :  Ave.  m.v.  is  the  average 
mean  variation  for  the  respective  points  in  terms  of  vibrations ; 
C.  E.  %  -f-,  the  per  cent,  of  individuals  who  made  a  constant  error 
in  the  direction  of  a  sharp ;  ^  — ,  the  per  cent,  of  those  who  flatted ; 
%  O,  the  per  cent,  of  those  who  made  no  appreciable  constant  error 
in  the  ten  trials;  C.  E.,  v.d.,  the  average  magnitude  in  vibrations  of 
the  constant  errors,  without  regard  to  sign ;  and  G.  C.  E.  v.d.  the 
tendency  of  the  constant  erors  for  the  group,  the  algebraic  mean. 
At  the  right,  the  grand  averages  for  both  groups  are  presented  under 
the  headings  designated  above. 

Comparison  of  the  abilities  of  men  and  women 

The  most  striking  general  feature  of  these  experiments  is  the 
the  fact  that  women  show  the  same  ability  as  men,  vibration  for 
vibration,  although  the  women  sang  an  octave  higher  than  the  men. 

The  data  on  which  this  assertion  is  based  may  be  traced  most 
readily  in  the  curves,  Figs.  5-8,  10.  In  Fig.  5  C.  it  is  seen  that  the 
curves  for  the  average  constant  errors  on  the  standard  as  well  as 
on  the  variant  practically  coincide.  On  the  standard  they  are 
almost  straight  lines,  the  variation  for  the  men  being  from  1.36  v.d. 
to  1.66  v.d.  with  an  average  of  1.54  v.d.,  while  in  the  case  of  the 
women  the  variation  of  this  measure  is  from  1.52  v.d.  to  1.81  v.d. 
with  an  average  of  1.65  v.d.  The  curves  for  the  variants  do  not 
come  so  near  coinciding;  they  are  of  the  same  form,  but  the 
women  have  the  advantage,  their  range  of  C.  E.  falling  between 
1.69  v.d.  and  6.71  v.d.  with  an  average  of  4.86  v.d.,  while  that  for 
the  men  lies  between  2.59  v.d.  and  7.15  v.d.  with  an  average  of 
5.32  v.d.    As  further  confirmation  of  the  fact  that  the  average  con- 

"  There  would  be  little  gained  by  placing  E.,  the  crude  error,  in  our  table  as 
this  measure  is  something  of  a  cross  between  C.  E.  and  m.v.  and  serves 
simply  to  indicate  the  distribution  of  the  constant  errors. 


50 


WALTER  R.  MILES 


0.5  O.d, 


Fig.  5.  The  data  in  Table  VIII.  If  there  had  been  no  errors  all  curves 
would  coincide  with  the  base  line.  The  amount  of  deviation  is  indicated  at 
the  left  in  terms  of  vibrations :  the  increments  on  the  base  line.  O  denotes 
the  standards  (128  v.d.  for  men  and  256  v.d.  for  women);  V  the  variants; 
C.  E.  average  (arithmetic)  constant  error;  G.  C.  E.  the  algebraic  constant 
error  or  general  tendency  of  the  group ;  and  m.v.  the  mean  variation. 
G.  C.  E.  above  the  base  indicates  plus  or  sharp  and  below  minus  or  flat. 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING 


51 


0-30  0Z3  on  0-iz  oB  ft?  03  c*2  or 
Fig.  6.  Intervals  as  sung.  (Table  VIII).  The  distribution  of  the  group 
constant  errors  (  G.  C.  E.  )  for  the  standards  (128  and  256  v.d.)  and  the 
variant  in  each  interval.  The  intervals  represented  by  the  forks  are  shown 
in  the  heavy  solid  curves  with  which  the  other  curves  would  coincide  were 
there  no  errors  in   singing. 


'6 

14 
IZ 
10 
6 
6 
<} 

Z 


-Men 

Women 


1    i  m\     \/  •■•'-'^ 


1     I 


../     I     I    V  I  \|— I— f— i---l 


u 


—  .  -f-  ''*-• 

x^d  10    1.5    20   15  3.0  JJ  W   45   50    5.5  6.0  65    7.0   7.5  80 

Fig.  7.     The  distribution   of  the  average  constant  errors  of   all   intervals 
for  each  observer  with  reference  to  the  magnitude  of  the  error.     The  data 
for   this    figure   are    found    in    the    columns    headed    Arithmetic    Average    in 
Table  VII.     O,  the  standard  tone:  V,  the  variant. 


52 


WALTER  R.  MILES 


Standard 
Variant 


^k  5  i^.-^   9.5  5  S5  6  65  7    75  Q   05  9  35  lO  lOSIt 


Fig.  8.     Distribution   of   constant   error,   flat   being   denoted  by 
the  base  and  sharp  by  -|-  above. 


—  below 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  53 

stant  errors  for  both  men  and  women  represent  approximately  equal 
magnitudes  attention  is  called  to  Fig.  7  in  which  is  presented  the 
distribution  of  the  average  constant  errors  of  all  intervals  for  each 
observer  with  reference  to  the  magnitude  of  the  error.  The  men  have 
a  slightly  better  record  on  the  O.  but  the  women  have  a  more  than 
compensating  advantage  on  the  V. 

A  corresponding  agreement  in  the  records  for  men  and  women 
is  seen  also  in  the  constant  tendency  for  the  group  (G.  C.  E.  Fig. 
5  A  and  B,  6,  and  8  A  and  B).  While  the  women  tend  to  sharp  and 
the  men  to  flat  on  the  standard  (see  Fig.  6)  the  amount  is  not  far 
from  equal  in  the  two  cases.  (Cf.  Table  VIII,  65  per  cent,  of  men 
flat  on  O  while  67  per  cent,  of  women  sharp).  In  view  of  the 
general  tendency  of  both  men  and  women  to  sharp  on  the  variant 
this  difi^erence  in  the  tendency  on  the  standard  gives  an  advantage 
to  the  women  as  regards  accuracy  in  the  singing  of  the  interval. 
An  advantage  which  amounts  to  an  average  of  over  2.0  v.d. 


Women 


O.d  10    1.5  Z.0   Z5  3.0   JS  W   f.5  SO  dS  6.0  6.5   7.0 


15 


Fig.  9.  The  distribution  of  the  mean  variation  (m.v.)  for  individuals 
(Table  VII,  average  m.v.  at  right)  with  reference  to  the  magnitude  of  the 
variations.     O,  m.v.  of  the  standard  tone;  V,  m.v.  of  the  variant. 

In  the  mean  variation  (Figs.  5  and  9),  which  is  an  important 
criterion,  the  advantage  is  more  clearly  in  favor  of  the  women, 
particularly  in  the  singing  of  the  variant.  There  are  more  men  than 
women  with  a  relatively  large  variation :  but  the  mode  in  the  case 
of  O  is  slightly  better  for  the  men  than  for  the  women.    The  averages 


54  WALTER  R.  MILES 

of  the  men  (Table  VIII)  are  1.54  and  3.05  v.d.  as  against  1.29  and 
2.21  v.d.  for  women. 

Taking  all  the  data  into  account  the  general  balance  of  all  scores 
results  practically  in  a  draw  :^^  men  and  women  sing  with  equal 
accuracy  (in  terms  of  number  of  vibrations  of  error)  although 
the  former  sing  at  128  v.d.  and  the  latter  at  256  v.d.  If  on  the 
other  hand  we  count  the  error  in  lelative  parts  of  a  tone  instead  of 
vibration  for  vibration,  the  women  sing  twice  as  accurately  as  the 
men.  It  may,  however,  be  shown  that  the  former  statement  repre- 
sents the  more  logical  point  of  view. 

This  result  is  in  harmony  with  the  results  found  in  Series  I  with 
reference  to  accuracy  within  the  tonal  range.  It  was  there  found 
that  so  long  as  the  singer  was  certainly  within  his  natural  range  the 
man  could  sing  the  two  tones  here  considered,  128  v.d.  and  256  v.d., 
with  nearly  equal  accuracy,  in  terms  of  vibrations  and  that,  there- 
fore, he  tended  to  sing  the  higher  twice  as  accurately  as  the  lower. 
The  difference  here  discussed  is  therefore  not  peculiarly  a  sex 
difference,  but  distinctly  a  matter  of  psycho-physic  law  of  voice 
control  within  the  tonal  range.  Men  and  women  have  equal  ability 
in  pitch  discrimination  (reference  21  p.  44),  so  also  in  voice  control 
they  have  equal  ability  level  for  level  within  the  tonal  range.  The 
fact  however  remains  that  women's  voices  are  pitched  in  a  higher 
register  than  men's  voices  and  therefore,  from  the  musical  point  of 
view,  they  can  sing  their  tones  relatively  more  accurately. 

This  result  is,  after  all  what  we  should  expect  for  the  principal 
limit  upon  accuracy  in  singing  is  accuracy  in  hearing  and  we  know 
that  both  men  and  women  can  hear  a  difference  of,  e.g.,  i  v.d.  as 
easily  at  256  v.d.  as  at  128  v.d. 

The  mean  variation 

Fig.  5  shows  that  the  mean  variation  is  larger  for  the  variants 
than  for  the  standards.  This  is  because  the  former  are  more 
difficult.  It  should  be  noted  that  this  difference  in  the  mean  varia- 
tion is  a  measure  of  the  relative  difficulty  of  the  two  tones  as  felt 

"The  following  facts  are  significant:  (i)  there  are  fewer  poor  observers 
among  the  women ;  (2)  women  have  smaller  mean  variations  than  men ;  and 
(3)  women  more  nearly  reproduce  the  intervals.  It  seems  quite  likely  that  in 
a  mixed  college  group  such  as  we  have  here,  the  women  give  more  attention 
to  vocal  music  than  do  the  men,  which  may  account  for  their  superiority 
in   this   test. 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  55 

and  would  also  be  a  measure  of  the  relative  degree  of  accuracy 
in  the  singing  of  them  were  it  not  for  the  operation  of  the  two 
motives  for  sharping  the  variant  about  the  middle  of  the  series  of 
the  increments.  The  fact  that  the  mean  variation  is  unaffected  by 
the  operation  of  these  two  motives  is  an  indication  of  their  fairly 
rigid  operation. 

The  constant  error 

Figs.  5  and  6  show  that  the  singing  of  the  standard  tone  is  not 
affected  by  the  magnitude  of  the  increment  to  be  sung.  The  constant 
error  is  small  and  uniform.  This  is  due  partly  to  the  fact  that  the 
standard  tone  was  the  same  in  all  trials  and  therefore  tended  to 
become  more  or  less  automatic,  and  partly  to  the  fact  that  the 
standard  was  sung  first  and  that  therefore  the  difficulty  in  marking 
off  the  interval  would  tend  to  crop  out  in  the  variant  tone. 

The  singing  of  the  variant  follows  the  law  that  ( i )  all  these  small 
increments  are  overestimated  and  that  (2)  this  overestimation  in- 
creases gradually  from  the  largest  interval  (0-30)  and  reaches  a 
maximum  in  the  cases  of  both  men  and  women  (Fig.  5,  A  and  B) 
at  the  5  v.d.  interval  from  which  it  gradually  again  diminishes. 

There  are  probably  several  motives  operating  to  produce  this 
overestimation;  the  fact  that  the  maximum  falls  in  the  increment 
5  v.d.  points  to  a  relationship  between  the  hearing  and  the  singing 
of  the  interval.  The  median  for  the  least  perceptible  difference  in 
pitch  for  this  same  group  of  individuals  falls  on  3  v.d.  The  incre- 
ment 5  v.d.  in  singing  would  therefore  represent  one  of  the  smallest 
increments  actually  heard.  The  distribution  around  this  would  be 
analogous  to  the  distribution  of  the  records  in  pitch  discrimination 
for  this  group. 

It  is  probable  that,  as  in  visual  perception  of  space,  all  small 
angles  are  overestimated,  there  is  in  hearing  of  pitch  a  tendency  to 
overestimate  the  smallest  increments  perceived.  If  we  represent  the 
uniformly  increasing  series  of  increments  of  pitch  difference  as  a 
sharp  wedge  the  apparent  magnitude  would  be  represented  by  a 
wedge  blunted  and  thickened. 

The  operation  of  such  a  principle  has  been  demonstrated  for  hear- 
ing in  the  matter  of  localization  of  sound.  Starch  (23)  found  that 
when  a  correction  is  made  for  the  least  perceptible  change  in  the 
direction  of  the  source  this  correction  is  always  overdone. 

The  lack  of  fine  control  of  the  voice  to  reproduce  the  smallest 


56  WALTER  R.  MILES 

differences  that  are  heard  is  another  element  involved.  This  factor 
is  partly  due  to  lack  of  knowledge  and  practice  in  this  kind  of  voice 
control.  The  small  differences  which  are  actually  heard  larger  than 
they  really  are,  are  sung  still  larger  on  account  of  this  general  lack 
of  control  for  the  making  of  fine  shadings  in  pitch.  This  overdoing 
of  a  difference  may  perhaps  be  regarded  as  another  phase  of  the 
same  principle  as  the  overestimation  of  small  differences  in  pitch  in 
hearing.  At  any  rate  the  enlarging  of  the  small  discriminated  in- 
crements is  without  doubt  much  increased  in  the  singing.  These 
small  increments  are  overestimated  in  hearing  (when  heard)  and  are 
again  overdone  in  the  singing;  and  that  this  enlarging  is  propor- 
tionate up  to  the  threshold  for  pitch  discrimination. 

In  applying  these  principles  to  the  interpretation  of  the  relative 
magnitude  of  the  errors  in  the  singing  of  these  increments  we  must 
bear  in  mind  that  where  the  small  differences  are  not  heard  there 
would  be  a  tendency  to  repeat  the  standard  in  trying  to  sing  the 
variant — this  happens  not  only  because  the  difference  is  not  heard, 
but  even  when  an  effort  is  made  to  sing  an  imperceptible  sharp 
theoretically  known  to  exist  there  is  a  tendency  for  the  voice  to 
"fall  into  the  groove"  of  the  standard  tone  which  has  been  sung  im- 
mediately  before. 

On  the  other  hand  it  seems  reasonable  to  take  account  of  the 
fact  that  in  this  test  we  are  asking  the  observer  to  do  something 
with  which  he  is  almost  entirely  unfamiliar.  In  the  larger  intervals 
he  recognizes  differences  but  overestimates  and  oversings  them. 
This  overestimation  increases  regularly  from  the  largest  interval, 
0-30,  to  0-5,  as  was  above  noted.  At  0-3  most  of  the  observers  fail 
to  hear  the  difference  because  the  conditions  of  the  test  do  not 
provide  the  immediately  successive  presentation  which  is  most  fav- 
orable for  the  discrimination  of  pitch  differences.  Therefore,  at 
0-3  failing  to  hear  the  second  fork  higher,  recognizing  that  he  has 
not  yet  reached  the  smallest  possible  interval,  and  knowing  that  the 
second  fork  is  higher  than  the  O,  our  observer  concentrates  his 
attention,  trying  harder  and  harder  until  the  last  interval  is  sung. 
He  is  in  large  measure  freed  from  the  factor  of  overestimation  in 
hearing  for  he  hears  no  difference.  He  will  very  likely  tell  you 
that  the  forks  sound  just  alike,  but  he  knows  and  is  reminded  that 
the  second  one  of  each  pair  is  higher.  This  knowledge  forms  the 
basis  of  his  control  of  the  voice.   Quite  naturally  under  the  circum- 


ACCURACY  OF   VOICE  IN  SIMPLE  PITCH  SINGING  57 

stances  he  resorts  to  the  tendency  (noted  above)  to  take  his  cue  for 
the  second  tone  not  from  the  fork  but  from  his  own  previous  tone. 
He  "falls  into  the  groove",  however,  just  long  enough  to  get  his 
bearings,  then  sharps  from  this  point,  the  magnitude  of  the  sharp 
being  governed  roughly  by  the  subject's  pitch  discrimination  ability. 
In  about  8  per  cent,  of  the  individual  records  of  0-.5  the  records  on 
the  .5  v.d.  are  not  sharp  or  may  be  slightly  fiat;  in  other  words,  the 
observers  took  the  risk  of  making  no  sharp. 

Applying  these  factors  in  the  interpretation  of  the  error  in  the 
singing  of  these  small  intervals  of  different  magnitude,  we  find  that, 
( I )  the  average  overestimation  is  relatively  small  for  the  smallest 
increments  because  in  many  cases  the  difference  is  not  heard  and  in 
singing  a  very  small  interval  the  voice  uses  its  previous  reproduction 
as  the  standard,  sharping  from  it,  and  (2)  the  overestimation  of 
the  small  increment  is  greatest  for  the  smallest  increments  per- 
ceived and  gradually  diminishes  as  the  increments  grow  larger  so 
that  it  tends  to  disappear  on  the  average  when  the  magnitude  of  a 
half-tone  is  reached.  Therefore,  our  test  seems  to  have  met  the 
conditions  for  measuring  the  minimal  producible  change  in  the 
pitch  of  the  voice.  The  increments  from  0-30  to  0-5  serve  to  work 
down  the  voice,  to  make  clear  to  the  observer  what  is  to  be  done, 
and  to  center  his  attention  for  most  careful  control.  The  four 
smaller  increments,  0-3  to  0-.5  are  the  place  where  the  "ability  to 
make  faint  shadings"  is  really  tested  and  under  usual  conditions 
the  reproductions  on  the  smallest  increment,  0-.5,  would  seem  to 
give  the  best  measure. 

If  from  the  records  on  0-.5  (algebraic  C.  E.  or  G.  C.  E.)  we 
compute  the  magnitude  of  the  smallest  interval  as  actually  produced 
by  the  individual  observers  and  distribute  these  magnitudes  accord- 
ing to  their  frequency,  we  have  the  curves  of  Fig.  12.  The  median 
value  of  the  measures  represented  in  Fig.  12  is  4.0  v.d.  for  women 
and  4.5  v.d.  for  men.  There  are  more  extremely  poor  observers 
among  the  men  so  that  the  average  smallest  intervals  produced  are 
5.6  v.d.  and  3.7  v.d.  for  men  and  women  respectively.^''  These  median 
values  are  in  harmony  with  the  results  for  pitch  discrimination  and 
may  be  taken  as  measures  of  the  ability  to  produce  minimal  changes 
sharp  or  flat  in  the  pitch  of  the  voice. 

'°A  part  of  this  difference  between  men  and  women  is  to  be  accounted 
for  in  the  fact  that  on  the  average  the  men  flatted  the  O. 


58 


WALTER  R.  MILES 


Dr.  D.  A.  Anderson  made  a  test  on  "minimal  change  in  the  pitch 
of  the  voice"  in  the  Iowa  Psychological  Laboratory  in  1909.  His 
observers  imitated  the  pitch  of  one  standard  fork  and  then  sang 
the  tone  the  least  possible  sharp  or  flat  according  as  directed,  making 
ten  successive  trials  in  each  direction.  There  were  115  women  and 
65  men  in  the  group  tested.  From  the  unpublished  results  of  this 
test  we  learn  that  the  average  minimal  producible  change  for  men 
was  5.5  v.d.  and  for  women  4.6  v.d  as  against  5.6  v.d.  and  2)-7  v.d. 
in  our  test.  In  comparing  these  results  it  must  however  be  noted 
that  45  of  Professor  Anderson's  poorest  observers,  most  of  them 
men,  made  no  records  which  entered  into  his  averages. 

Seashore  (19)  reports  the  results  of  some  tests  of  "minimal 
prpducible  change"  given  to  a  small  group  of  observers.  The 
average  records  for  six  men  on  five  successive  days  are  as  follows ; 
3.4.  3.5,  3.0,  2.6,  and  2.7  v.d.  Evidently  the  factor  of  practice  entered 
here.  However,  the  average  of  these  results,  which  represents 
the  only  other  available  data  on  this  ability  in  voice  control,  falls 
on  the  mode  of  our  curve   (Fig.   12)    for  men. 


/O    II    IZ    /J    14    15 


Fig.  10.  Distribution  of  the  magnitudes  of  the  smallest  interval  actu- 
ally produced  by  men  and  women.  The  method  of  computing  the  average 
magnitude  of  the  smallest  interval  produced  by  each  observer  is  illustrated 
in  the  following  example:  if  the  C.  E.  on  O  is  —.9  v.d.  and  on  V  is  +1.4  v.d. 
then  the  produced  interval  would  equal  the  difference  between  —.9  v.d.  and 
+1.4  v.d.  plus  .5  v.d.  (the  real  step  between  the  forks)  =  2.8  v.d.  If  the 
C.  E.  on  O  is  plus  it  is  of  course  subtracted  from  the  sum  of  C.E.  on  V 
and  .5  v.d.     Men  dotted  line;  women  broken  line. 

The  average  constant  error  (C.  E.)  on  the  standard  is  small  and 
uniform,  as  is  also  the  mean  variation  and  the  constant  tendency 
for  the  group,  (G.  C.  E.  on  the  standard).  Accuracy  in  the  stand- 
ard is  not  influenced  by  any  difference  in  the  magnitude  of  the  in- 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING 


59 


crements.  This  is  chiefly  because  the  standard  tone  was  sung  before 
the  variant  was  sounded,  and  partly  because  a  sort  of  "rut"  was 
formed  for  the  singing  of  the  repeated  standard. 

The  researches  previously  reviewed  contain  scattered  measures 
on  this  ability.  Kliinder  (i)  found  that  he  could  reproduce  an 
organ  tone  of  128  v.d.  with  an  average  crude  error  of  .47  v.d.  He 
rejected  however  the  records  of  some  other  observers  who  showed 
larger  errors.  Cameron  (4)  worked  with  seven  observers  and  tried 
a  number  of  organ  tones.  The  records  by  three  of  these  observers 
gave  an  average  error  of  about  6.6  v.d.  Berlage  (2),  whose  three 
observers  reproduced  voice  tones,  does  not  give  the  pitch  of  the 
standards.  The  average  error  for  the  three  men,  singing  with  an 
interval  of  from  i  second  to  2  seconds,  is  .50  v.d.^'  Seashore  (19) 
gives  1.2  v.d.  as  the  average  error  of  100  trials  by  each  of  six  men,  on 
standard  100  v.d.  Sokolowsky  (22)  with  his  seven  professional 
singers  finds  an  average  error  of  i  v.d.  at  the  average  pitch  of 
251  v.d. 

The  group  constant  error 

Throughout  the  previous  pages  there  have  been  references  to  the 
tendency  of  both  men  and  women  to  sing  sharp  when  reproducing  a 
tone.  The  difference  in  the  direction  of  this  error  in  the  standard 
for  men  and  for  women  is  so  constant  that,  while  small,  it  points 
to  some  motive  in  the  character  of  the  tone,  the  mode  of  singing,  or 
some  tendency  characteristic  of  a  given  pitch  level.  The  distribution 
seen  in  Figs.  7  and  8  shows  that  the  sharps  and  the  flats  are  not  far 
from  equal  both  in  the  number  and  the  magnitude  for  men;  for 
women  the  sharps  predominate  in  both  magnitude  and  number. 

Cameron  (4)  noticed  this  tendency  and  called  attention  to  it. 
In  his  experiments  it  appeared  especially  in  sustained  tones. ^"^  We 
have  not   worked  with   sustained   tones  but  have  found  the  same 

^'  Berlage's  tables  are  needlessly  complicated  by  his  using  the  signs  with 
opposite  from  the  usual  meaning. 

^'^  Berlage  (2)  did  not  find  this  tendency  to  sharp  and  was  surprised,  but 
we  must  remember  that  he  worked  with  voice  tones  for  standards  (the 
richest  tone  possible)  and  our  experiments  seem  to  show  that  with  rich 
standard  tones  the  sharping  of  the  constant  error  is  considerably  decreased. 
Sokolowsky's  (22)  results  are  also  negative  as  regards  any  general  ten- 
dency for  both  sexes  to  sing  sharp.  The  errors  on  the  twenty  tones  sung 
by  women,  however,  shozv  an  algebraic  average  of  +/.oj  z'.d..  although 
eleven     of  these  tones  were  sung  flat. 


6o  WALTER  R.  MILES 

tendency  with  reproductions  of  one  and  two  seconds  in  length. 
Reference  to  our  tables  (G.  C.  E.)  will  show  that  almost  without 
exception  sharping  is  the  predominant  direction  of  the  constant 
errors  in  all  six  series  of  our  experiments.  The  tendency  to  sing 
sharp  is  not  materially  alTected  by  the  level  of  the  pitch  so  long  as 
the  tone  remains  within  the  range  of  the  voice ;  it  is  increased  by  loud 
volume  of  voice,  weak  volume  of  standard,  certain  vowel  formants 
such  as  are  found  in  "e"  and  "i'",  and  by  purity  of  the  standard 
tones. 

The  best  cases 

The  question  naturally  arises,  to  what  extent  the  presence  of  a 
few  cases  of  very  large  error  affect  the  averages.  To  cast  some 
light  on  this  and  also  to  gain  an  idea  of  the  performance  of  the  best 
observers  in  the  group  the  author  made  a  selection  of  twenty-five 
persons  of  each  sex.  The  selection  was  made  chiefly  on  the  basis 
of  a  small  Ave.  m.v.  in  the  standard  (o).  The  size  of  the  Ave.  C.  E. 
of  o  and  the  Ave.  m.v.  for  the  increments,  were  used  as  secondary 
criteria.  There  are  some  records,  for  example  N.  9,  which  from  the 
standpoint  of  the  constant  errors  alone  are  very  near  the  ideal  curves, 
but  because  of  rather  large  mean  variations  must  be  omitted  from 
these  selected  groups.  The  selection  of  women  was  as  follows : 
Nos.  I,  3,  13,  15,  21,  55,  61,  63,  77,  85,  93,  97,  105,  107,  113,  117, 
125,  153,  159,  169,  177,  181,  183,  201,  and  209.  The  men's  records 
chosen  were:  Nos:  6,  8,  10,  12,  16,  28,  50,  62,  68,  72,  82,  88,  102, 
106,  no,  114,  120,  126,  128,  144,  146,  148,  154,  156,  and  164. 

The  separate  tabulation  of  these  fifty  supposedly  best  cases  re- 
veals the  presence  of  the  same  general  tendencies  in  these  selected 
groups  as  have  been  noted  in  the  large  groups,  with  the  difference 
that  they  are  not  so  pronounced  and  that  here  the  men  in  a  relative 
comparison  make  a  better  showing  than  the  women,  in  that  their 
overestimation  especially  of  the  smaller  pitch  increments  is  less. 
Therefore  blame  for  the  large  errors  (overestimation  of  intervals) 
can  hardly  be  shifted  to  a  few  individuals  as  indeed  we  might  have 
shown  by  referring  to  Figs.  7  and  8  which  demonstrate  that  the 
distribution  of  the  errors  forms  fairly  normal  frequency  curves. 

Correlation   of  singing   zvith   pitch    discrimination 

Pitch  discrimination  records  are  available  for  eighty-two  of  the 
men,  and  one  hundred  and  four  of  the  women  V\^ho  acted  as  observers 


ACCURACY   OF   VOICE  IN  SIMPLE  PITCH  SINGING         6i 

in  our  tests.     The  well-known  formula  of  the  Pearson  "Product- 
Moments"  was  employed  and  resulted  in  the  following  correlations : 

r    P.E.r 
Men:         Size  of  ave.  smallest  interval  produced  with  Pitch.  Disc.  +.21     .072 


Women  : 


m.v.  on  0. 

u 

il               i 

+.04 

.074 

C.E.  on  0. 

u 

n                  > 

'    +.08 

.074 

m.v.  on  V. 

(t 

it               i 

+.33 

.066 

C.E.  on  V. 

it 

ti 

'    +.15 

.073. 

smallest    interval 

produced 

n 

it 

"  —.11 

.065 

m.v.  on  0. 

it 

il              • 

+.27 

.061 

C.E.  on  0. 

ti 

ti               t 

+.11 

.065 

m.v.  on  V. 

« 

it              < 

+.51 

.048 

C  E.  on  V. 

« 

it 

'  -.07 

.065 

It  will  be  recalled  that  in  order  to  be  satisfactory  a  coefficient 
"should  be  perhaps  three  to  five  times  as  large"  as  its  probable  error. 
This  rule  liberally  applied  to  our  results  leaves  us  the  coefficients 
-I-.33  and  -(-.51  both  of  unquestionable  reliability.  These  coefficients 
represent  the  correlation  between  pitch  discrimination  and  the  aver- 
age mean  variation  in  singing  the  intervals,  for  men  and  women 
respectively. 

The  Test  of  ipio 

A  series  of  musical  tests,  given  by  the  writer  in  the  Iowa  Psycho- 
logical Laboratory,  during  November  and  December  of  1910,  in- 
cluded one  on  Accuracy  in  Reproducing  Tones.  There  were  ninety 
men  and  one  hundred  and  seven  women,  members  of  the  elementary 
psychology  classes  who  took  this  test. 

The  apparatus  besides  the  tonoscope  consisted  of  five  large  forks 
with  pitches  as  follows:  128,  256,  320,  384,  and  512  v.d.  The  ex- 
perimenter instructed  the  observer  to  take  the  256  v.d.  fork,  strike 
it  gently,  bring  it  to  his  ear,  listen  carefully,  and  then  to  reproduce 
the  same  pitch.  This  he  repeated  with  fork  256  v.d.  Then  taking 
the  320  v.d.  fork  he  proceeded  as  described.  The  last  four  forks 
were  gone  over  five  times  in  this  manner,  which  gives  ten  trials 
on  each  tone,  forty  trials  in  all.  The  test  is  thus  very  simple,  the  re- 
production of  four  tones  (two  successive  trials  on  each)  which 
are  at  the  same  time  natural  musical  intervals:  major  third,  fifth  and 
octave.  No  restrictions  were  placed  upon  the  observer  in  the  matter 
of  humming  or  singing  with  the  standards.  As  the  fork  was  in  his 
hand  he  sang  with  it  or  after  it  as  seemed  best  to  him.  About  one- 
half  the  observers  preferred  to  take  the  fork  away  from  the  ear 
before  beginning  to  sing.    The  men  sang  the  tones  one  octave  below 


62  WALTER  R.  MILES 

the  pitch  of  the  fork.  When  it  was  difficult  for  them  to  commence 
doing  this,  the  128  v.d.  standard  was  used  for  orientation. 

The  results  for  this  series  of  8,000  reproductions  are  given  in 
Table  IX.  The  notation  is  the  same  as  in  Table  VIII.  The  test  of 
19 10  was  complicated  by  the  factor  of  natural  musical  intervals,  it 
was  also  considerably  shorter  and  simpler  than  the  one  of  1913  but 
in  comparing  it  with  the  latter  we  find  the  results  in  practical  agree- 
ment on  some  points. 

(i).  There  is  a  uniform  tendency  for  the  majority  of  observers 
to  sing  sharp.  Here  again  the  tendency  appears  to  be  greater  for 
women  than  for  men,  the  G.  C.  E,  for  men  being  +.26  v.d.,  for 

TABLE  IX.     Accuracy  of  singing:   test  of  1910 


90  men  128  v.d. 

160  v.d. 

192  v.d. 

256  v.d. 

Ave.  m.v.    1.42 

1.36 

1.43 

1.79 

%  +  C.  E.    47 

63 

51 

63 

%  -  C.  E.    S3 

37 

49 

37 

Av  C.  C.    1.62 

1.62 

1.72 

2.70 

G.  C.  E.    +  .26 

+  .65 

—  .06 

+  1.06 

107 

women  256  v.d. 

320  v.d. 

384  v.d. 

512  v.d. 

Ave.  m.v.    1.89 

2.15 

2.07 

2.83 

%  +  C.  E.    81 

90 

84 

86 

%  —  C.  E.    19 

10 

16 

14 

Av.  C.  E.    2.59 

3-91 

3-47 

5 -90 

G.  C.  E.    +2.39 

+3-36 

+3.1 1 

+4.76 

women  -|-  2.39  v.d.,  a  difference  of  2.13  v.d.  as  contrasted  with  1.30 
v.d.  in  the  previous  measurements.  In  the  test  of  1910,  as  mentioned, 
the  men  and  women  used  the  same  forks,  the  men  singing  the  stand- 
ards one  octave  low.  Therefore  the  tendency  for  men  to  sing  less 
sharp  than  women  in  the  1913  experiments  can  hardly  be  attrabuted 
to  a  timbre  or  sound  volume  difference  between  the  sets  of  forks. 
The  men  are  must  more  evenly  divided  between  the  sharping  and 
flatting  tendencies  than  the  women,  for  example  on  256  v.d.  the  one 
tone  which  both  sexes  had  in  common,  the  percentages  in  favor  of 
sharping  are  63  and  86  for  men  and  women  respectively.  (2)  The 
average  constant  error  (arithmetic)  on  128  v.d.  is  slightly  larger  in 
1910,  1.62  v.d.  as  against  1.54  v.d.  The  mean  variation  for  128  v.d. 
are  1.42  v.d.  (1910)  and  1.54  v.d.  These  differences  are  rather 
slight.     (3)   Men  and  women  sing  their  one  common  tone  (256  v.d.) 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  63 

with  equal  accuracy:  m.v.  1.79  v.d.,  Av.  C.  E.,  2.70  v.d.  (men)  to 
m.v.,  1.89  v.d.,  Av.  C.  E.  2.59  (women).  It  would  seem  from  a  com- 
parison of  available  norms  for  voice  range  in  the  sexes  (Helm- 
holtz  (9)  and  Zahm  (27)  that  256  v.d.  should  be  about  as  high  for 
men  as  it  is  low  for  women,  and  that  it  is  well  within  the  average 
range  of  both.  We  have  here  therefore  a  confirmation  of  our 
previous  conclusion,  i.e.,  that  men  and  women  sing  with  equal 
accuracy  vibration  for  vibration.  However  the  errors  in  this  case 
under  consideration  (1910)  are  much  larger  than  the  results  of 
Series  VI  would  lead  us  to  expect.  This  is  true  of  all  the  tones 
sung  by  the  women  and  renders  them  incomparable  with  the  pre- 
vious results. 

Recommendations  toward  a  standard  test 
The  recommendations  which  follow  must  be  considered  as  pre- 
liminary and  as  applying  simply  to  the  two  measures  of  singing 
ability  considered  throughout  this  study,  i.e.,  the  ability  of  the 
voice  to  reproduce  pitch,  and  the  ability  to  produce  voluntarily 
small  changes  sharp  or  flat  in  the  pitch  of  the  voice. 

1.  The  two  factors  may  be  tested  together  with  advantage.  They 
are  closely  related  phases  of  the  same  thing.  Neither  of  them  should 
be  taken  in  combination  with  such  factors  as  accuracy  of  tone  mem- 
ory, or  judgment  for  musical  intervals. 

2.  Use  a  graded  series  of  standard  tones  similar  to  that  commonly 
employed  in  testing  for  pitch  discrimination.  Such  a  series  has  ob- 
vious advantages  over  the  use  of  a  single  standard;  (i)  If  several 
observations  are  to  be  made  at  a  single  sitting  the  efifects  of  practice 
are  not  so  great.  (2)  The  small  pitch  intervals  make  clear  to  the  ob- 
server what  he  is  expected  to  do  with  his  voice.  (3)  The  variety 
of  standards  (and  hence  degrees  of  difficulty)  reduce  monotony 
and  fatigue.  A  graded  series  furthermore  has  advantage  over 
any  other  series :  ( i )  it  keeps  the  test  comparatively  free  from 
complication  with  the  singing  of  musical  intervals,  and  (2)  when 
the  standards  represent  small  steps  of  pitch  difiference  the  observer 
discriminates  more  carefully  and  is  not  so  Hkely  to  be  satisfied  with 
a  mere  approximation. 

3.  Use  tuning  forks  for  standards.  They  are  very  easily  manip- 
ulated, are  not  subject  to  certain  sources  of  error  commonly  met  in 
the  control  of  reeds,  pipes  and  strings,  and  are  readily  arranged 


64  WALTER  R.  MILES 

into  a  graded  series  as  recommended  above.  Any  disadvantage,  if 
indeed  it  may  be  so  called,  from  the  standpoint  of  the  purity  of  the 
fork  tone  seems  more  than  compensated  for  in  having  a  definable 
quality  and  a  standard  on  which  all  observers  are  equally 
unpracticed. 

4.  Begin  with  the  largest  pitch  increments  and  proceed  to  the 
smallest  and  then  in  reverse  order  back  to  the  largest.  This  will 
economize  effort,  provide  the  best  practice,  and  help  to  control  tha 
attention.  For  general  testing  ten  intervals  representing  as  many 
degrees  of  difficulty,  ranging  from  0-30  to  0-.5  are  not  too  many. 
For  extensive  testing  of  one  observer  or  in  working  with  highly 
practiced  observers  the  increments  which  are  distinctly  above  the 
threshold  for  pitch  discrimination  may  be  omitted. 

5.  Give  the  tones  in  pairs,  presenting  the  variant  tone  imme- 
diately after  the  reproduction  of  the  standard,  thus  securing  a  rapid 
adjustment  which  favors  discrimination  in  the  kinaesthetic  sensations 
from  the  larynx.  As  an  alternative  procedure  the  two  tones 
might  be  presented  in  immediate  succession  as  in  the  pitch  discrim- 
ination tests,  the  observer  carrying  the  standard  in  mind  while 
listening  to  the  variant,  and  then  singing  them  in  quick  succession. 

6.  Control  conditions :  ( i )  The  forks  should  be  presented  be- 
fore resonators  which  are  some  distance  from  the  observer  and  care 
must  be  exercised  to  present  them  with  uniform  intensity.  (2) 
The  observer  should  use  a  medium  volume  of  voice  in  singing  the 
tones.  (3)  The  experimenter  should  select  the  vowel  to  be  sung 
and  insist  on  a  good  quality.  (4)  If  time  intervals  are  used  be- 
tween standards  and  reproductions  they  should  be  short,  not  longer 
than  two  seconds  at  most.  (5)  Time  intervals  should  be  introduced 
between  pairs  of  tones.  These  should  be  at  least  2  seconds  in  length. 
Longer  intervals  would  doubtless  be  better  as  the  voice  could  the 
more  easily  be  kept  out  of  a  "rut"  in  reproducing  the  standard. 
(6)  Secure  effort  on  the  part  of  the  observer  who  is  too  easily 
satisfied  with  his  own  performance. 

Our  test  is  one  of  motor  control.  As  a  musical  test  it  bears  the 
same  relation  to  the  motor  side  as  pitch  discrimination  does  to  the 
sensory  side.  In  fact  it  is  in  a  practical  way  for  the  motor  pitch  dis- 
crimination of  the  singer,  and  as  far  as  singing  is  concerned  it  is 
more  important  than  simple  sensory  pitch  discrimination. 


ACCURACY  OF  VOICE  IN  SIMPLE  PITCH  SINGING  65 

SUMMARY  OF  CONCLUSIONS 
Among  others  the  following  general  conclusions  may  be  gleaned 
from  the  foregoing  experiments. 

1.  The  human  voice  is  about  equally  accurate,  in  terms  of  vibra- 
tion, at  all  points  well  within  its  range ;  therefore,  the  high  tones  are 
sung  relatively  (per  cent.)  more  exactly  than  those  which  are  low. 

2.  A  strong  standard  tone  (especially  with  low  forks)  is  repro- 
duced as  decidedly  lower  than  a  weak  standard. 

3.  The  voice  can  most  easily  reproduce  pitch  for  those  standard 
tones  which  have  a  rich  timbre,  such  as  the  organ  tone. 

4.  Measured  in  terms  of  average  error  the  voice  is  less  accurate 
when  its  volume  is  large. 

5.  Vowel  quality  affects  the  accuracy  of  vocal  reproduction  of 
tones.  The  "a'"  (as  i  in  machine)  is  reproduced  the  highest,  "0" 
the  lowest,  and  "a"  occupies  a  middle  position. 

6.  Men  and  women  sing  in  their  representative  ranges  with  equal 
accuracy  vibration  of  error. 

7.  Women  show  better  relative  voice  control  than  men,  if  judged 
on  the  basis  of  their  mean  variation. 

8.  With  women  there  is  a  general  tendency  to  sing  sharp.  Men 
are  about  equally  divided  in  this  regard,  sharping  however  being 
slightly  more  frequent. 

9.  The  average  error  of  the  voice  in  reproducing  a  tone  given 
by  a  fork  is  1.5  v.d.  for  men  at  range  128  v.d.,  and  1.5  v.d.  for 
women  at  256  v.d.  in  a  representative  group  of  students. 

10.  A  small  perceptible  pitch  difference  between  two  tones  is 
overestimated  in  the  singing. 

11.  The  average  minimal  producible  change  of  the  voice  for  men 
at  128  v.d.  is  about  5.5  v.d.,  and  for  women  at  256  v.d.  it  is  3.5  v.d. 

REFERENCES 

1.  Anderson,  D.  A.  The  Effect  of  Intensity  on  the  Apparent 
Pitch  of  Tones  in  the  Middle  Range.     (In  this  Volume.) 

2.  Blake,  The  Use  of  the  Membrana  Tympani  as  a  Phonauto- 
graph  and  Logograph.    Arch,  of  Opthal.  and  Otol.,  1876.  V. 

3.  Berlage,  F.  Der  Einfluss  von  Artikulation  und  Gehor  beim 
Nachsingen  von  Stimmklangen.  Psychol.  Stud.,  1910,  VI, 
39-140. 

4.  Cameron,  E.  H.  Tonal  Reactions.  Psychol.  Rev.,  Monog. 
Suppl,  1907,  VIII,  227-300. 

5.  Grutzner,  Die  Stimme.    1907. 


G6  WALTER  R.  MILES  ^ 

6.  Guttman,  A.  Zur  Psychophysik  des  Gesanges.     Zsch.  f.  Psy- 
chol, u.  Physiol,  d.  Sinnes.,  1913,  LXIII,  161-176. 

7.  Gutzmann,   H.   A.   K.     Physiologie  der  Stimme  und  Sprache. 
Braunschweig,  1909. 

8.  Hancock,  C.  L.    The  Effect  of  Intensity  on  the  Apparent  Pitch 
of  Tones  in  the  Lower  Range.     (In  this  Volume.) 

9.  Helmholtz,  H.    Sensations  of  Tone.    Tr.  by  Ellis  1895. 

10.  Hensen.  Ein  einfaches  Verfahren  zur  Beobachtung  der 
Tonhohe  eines  gesungen  Tons.  Arch.  f.  Anat.  u.  Physiol. 
(Physiol.  Abth.),  1879,  pp.  155  ff. 

11.  Kliinder,  A.  Ein  Versuch  die  Fehler  zu  bestinimen  welche 
der  Kehlopf  beim  Halten  eines  Tones  macht.  Inaug.  Disserta- 
tion, Marburg,  1872. 

12.  Kliinder,  Ad.  Ueber  die  Genauigkeit  der  Stimme.  Arch.  f. 
Anat.  u.  Psychol.,  Du  Bois  Reymond,  (Physiol.  Abth.)  1879, 
pp.  119,  ff. 

13.  Luft,  E.  Ueber  die  Unterschiedsempfindlichkeit  fiir  Tonhonen, 
Phil.  Stud.  1888.  IV,  511-540. 

14.  Marbe,  K.  Uber  die  Verwendung  russender  Flammen  in  der 
Psychologic  und  deren  Grengebieten,  Zsch.  f.  Psychol.,  1908, 
XLVIX,  206-217. 

15.  Meyer,  Max.  Ueber  die  Unterschiedsempfindlichkeit  fiir  Ton- 
hohen,  Ztsch.  f.  Psychol.,  1898,  XVI,  352-372. 

16.  Preyer,  .... 

17.  Scott.  Inscription  automatiqne  des  sons  de  I'air  au  moyen 
d'nne  orellc  artificielle.    1861. 

18.  Scripture,  E.  W.  Researches  in  Experimental  Phonetics. 
Carnegie  Institution,  1906. 

19.  Seashore,  C.  E.  and  Jenner,  E.  A.  Training  the  Voice  by  the  Aid 
of  the  Eye  in  Singing.     /.  of  Educ.  Psychol.,  1910,  I,  311-320. 

20.  Seashore,  C.  E.  A  Voice  Tonoscope.  Iowa  Stud,  in  Psychol., 
1902,  III,  18  ff. 

21.  Seashore,  C.  E.  The  Measurement  of  Pitch  Discrimination:  A 
Preliminary  Report.    Psychol.  Monog.,  XIII,  21-60. 

22.  Sokolowsky,  R.  Ueber  die  Genauigkeit  des  Nachsingens  von 
Tonen  bei  Berufssangern.  Beitr.  z  Anat.,  Physiol.,  Path,  usw. 
von  Passow  u.  Schaefer.,  1911,  V. 

23.  Starch,  D.  Perimetry  of  the  Localization  of  Sound.  (lozm 
Stud,  in  Psychol.,  V,  1-55)  Psychol.  Rev.  Monog..  IX. 

24.  Stern,  H.  Gesangphysiolgie  und  Gesangpadogogik  ihren 
Beziehungen  zur  Frage  der  Muskelempfindungen  und  der  beim 
Singen  am  Schadel  und  am  Thorax  fiihlbaren  Vibrationen. 
Monat.  f.  Ohrenhk.,  1912,  XLVI,  337-352. 

25.  Stumpf,  C.     Tonpsychologie.     1883. 

26.  Vance,  T.  F.  Pitch  Discrimination  within  the  Tonal  Range. 
(In  this  Volume.) 

27.  Zahm,  J.  A.     Sound  and  Music.    Chicago;  McClurg  1892. 


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